<PAGE>   1

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
                            ------------------------

                                    FORM 10-K

ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES  EXCHANGE ACT 
OF 1934 [FEE REQUIRED].

For fiscal year ended, SEPTEMBER 30, 1998      Commission file number    1-9965
                       ------------------                                ------

                           KEITHLEY INSTRUMENTS, INC.
-------------------------------------------------------------------------------
             (Exact name of registrant as specified in its charter)

              OHIO                                 34-0794417
-----------------------------------------  ------------------------------------
(State of incorporation or organization)   (I.R.S. Employer Identification No.)

28775 AURORA ROAD, SOLON, OHIO                                 44139
---------------------------------------                     -----------
(Address of principal executive offices)                     (Zip Code)

Registrant's telephone number, including area code   (440) 248-0400
                                                   -------------------

Securities registered pursuant to Section 12(b) of the Act:

COMMON SHARES, WITHOUT PAR VALUE                NEW YORK STOCK EXCHANGE
-----------------------------------      ---------------------------------------
         (Title of each class)           (Name of exchange on which registered)



Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months, and (2) has been subject to such filing requirements
for the past 90 days. Yes X   No
                      -----     -----

Indicate by check mark if disclosure of delinquent filers pursuant to Item 405
of Regulation S-K is not contained herein, and will not be contained, to the
best of the registrant's knowledge, in definitive proxy or information
statements incorporated by reference in Part III of this Form 10-K or any
amendment to this Form 10-K. [X]
                             ----

As of December 15, 1998 there were outstanding 4,784,812 Common Shares, without
par value, and 2,692,528 Class B Common Shares, without par value. At that date,
the aggregate market value of the Common Shares of the Registrant held by
non-affiliates was $34,434,157 and the aggregate market value of the Class B
Common Shares of the Registrant held by non-affiliates was $332,801 for a total
aggregate market value of all classes of Common Shares held by non-affiliates of
$34,766,957. While the Class B Common Shares are not listed for public trading
on any exchange or market system, shares of that class are convertible into
Common Shares at any time on a share-for-share basis. The market values
indicated were calculated based upon the last sale price of the Common Shares as
reported by the New York Stock Exchange on December 15, 1998, which was $7.75.
For purposes of this information, the 341,695 Common Shares and 2,649,586 Class
B Common Shares which were held by the officers and Directors of the Company
were deemed to be voting stock held by affiliates.

                       DOCUMENTS INCORPORATED BY REFERENCE

Portions of the following documents are incorporated by reference into the
designated parts of this Form 10-K: 

DOCUMENT                                                        Part of 10-K 

1.  Annual report to shareholders for the fiscal                Parts I and II
    year ended September 30, 1998 
2.  Proxy statement for the annual meeting of shareholders      Part III
    to be held on February 13, 1999 
With the exception of the information specifically incorporated by reference,
neither the Company's proxy statement nor the 1998 annual report to shareholders
is deemed to be filed as part of this Form 10-K.



<PAGE>   2



                           KEITHLEY INSTRUMENTS, INC.

                               10-K ANNUAL REPORT


                                TABLE OF CONTENTS

<TABLE>
<CAPTION>
PART I:                                                                                             PAGE
-------                                                                                             ----
<S>      <C>                                                                                      <C>
         Item 1.           Business                                                                   1
         Item 2.           Properties                                                                 8
         Item 3.           Legal Proceedings                                                          9
         Item 4.           Submission of Matters to a Vote of Security Holders                        9

PART II:

         Item 5.           Market for the Registrant's Common Equity and Related
                             Stockholder Matters                                                     11
         Item 6.           Selected Financial Data                                                   11
         Item 7.           Management's Discussion and Analysis of Financial
                             Condition and Results of Operations                                     11
         Item 8.           Financial Statements and Supplementary Data                               11
         Item 9.           Changes in and Disagreements with Accountants on
                             Accounting and Financial Disclosure                                     11

PART III.

         Item 10.          Directors and Executive Officers of the Registrant                        12
         Item 11.          Executive Compensation                                                    12
         Item 12.          Security Ownership of Certain Beneficial Owners and
                             Management                                                              12
         Item 13.          Certain Relationships and Related Transactions                            12

PART IV:

         Item 14.          Exhibits, Financial Statement Schedules and Reports on
                             Form 8-K                                                                13
</TABLE>



<PAGE>   3



                                   PART I.

ITEM 1 - BUSINESS.

GENERAL

         Keithley Instruments, Inc. is a corporation which was founded in 1946
and organized under the laws of the State of Ohio on October 1, 1955. Its
principal executive offices are located at 28775 Aurora Road, Solon, Ohio 44139;
telephone (440) 248-0400. References herein to the "Company" or "Keithley" are
to Keithley Instruments, Inc. and its subsidiaries unless the context indicates
otherwise.

RECENT EVENTS

         On August 10, 1998, the Company sold the principal assets used in the
operation of its Radiation Measurements Division to Inovision Radiation
Measurements, L.L.C for $8.7 million in cash. The agreement was effective July
31, 1998. Prior to its sale, the Radiation Measurements Division developed,
manufactured and marketed products and systems that accurately measure the
radiation emission levels of x-ray machines and nuclear radiation sources and
were used to calibrate radiation therapy and x-ray equipment in hospitals and
manufacturing processes. The Division accounted for approximately eight percent
of the Company's fiscal 1998 net sales.

SUBSEQUENT EVENTS

         On November 9, 1998, the Company sold the principal assets used in the
operation of its Quantox oxide monitoring product line to KLA-Tencor Corporation
for $9.1 million in cash. The agreement was effective October 31, 1998. The
Quantox product line had been sold to semiconductor manufacturers and
represented approximately ten percent of the Company's fiscal 1998 net sales.

         On November 11, 1998, the Company commenced a tender offer to
repurchase up to 2,000,000 of its Common Shares, or approximately 40 percent of
Common Shares outstanding (25 percent of Class B and Common Shares combined).
The offer was conducted through a procedure commonly known as a "Dutch Auction"
in which shareholders could tender their shares at prices not in excess of $7.00
nor less than $5.75 per share. The offer expired on December 10, 1998, at which
time the Company accepted for purchase and purchased 405,757 Common Shares, or
approximately eight percent of the outstanding Common Shares (five percent of
Class B and Common Shares combined), for $7.00 per share.

PRODUCTS

         Keithley Instruments, Inc. provides electrical measurement solutions to
wireless communications, semiconductor and electronic component manufacturers,
other high-growth areas of the electronics industry and research laboratories.
Engineers and scientists around the world use Keithley's advanced hardware and
software for process monitoring, production test and basis research. Although
the Company's products vary in capability, sophistication, use, size and price,
they basically test, measure, and analyze electrical and physical properties. As
such, the Company considers its business to be in a single industry segment. For
each of the 


                                       1
<PAGE>   4


last three fiscal years, more than 90% of the Company's revenue was
derived from the sale of electronic test and measurement instrumentation and
data acquisition and analysis hardware and software, which represents one class
of similar products.

         The product groups of the Company are described below:

         TEST AND MEASUREMENT. Test and Measurement designs, develops,
manufactures and markets sensitive electronic benchtop instrumentation and PC
board-level products used in production test, research and data acquisition and
analysis. These products measure a wide range of electrical properties such as
voltage, resistance, current, capacitance and charge. Benchtop instruments
generally range in price from $1,000 to $10,000 and PC board-level products
generally range in price from $100 to $4,000. Test and Measurements is composed
of the following product groups:

             DIGITAL MULTIMETERS. This product line includes a range of
             instruments that are designed to cover measurements of voltage,
             resistance, and current for production test, design and
             development, and research applications. Each digital multimeter has
             a computer interface for integration into automated test and
             measurement systems. Typical applications include testing
             electrical components such as resistors and thermistors, and end
             products which include cellular telephones, computer disk drives,
             and pace makers. These products are marketed primarily through
             direct marketing and personal selling.

             SENSITIVE INSTRUMENTS. This product group includes electrometers,
             picoammeters, sensitive digital voltmeters, micro-ohmmeters, and
             certain other instruments which are distinguished by their extreme
             sensitivity, resolution and accuracy as compared to the
             capabilities of conventional meters. Sensitive instruments are used
             by scientists, engineers, and researchers for the study of
             materials, semiconductors, and superconductors. Typical customers
             are industrial and government research laboratories, educational
             institutions, and electronics manufacturers. These products are
             marketed primarily through direct marketing and catalog mailings.

             SWITCHES AND SOURCES. Switching instruments are used to route
             electrical signals in test systems to measurement and source
             instrumentation. This allows many devices or test points to be
             measured with a minimum number of instruments. Switch products
             together with Sensitive, Digital Multimeter, Source, I-V and C-V
             instruments can be integrated into computer-based systems to
             provide flexible, automated testing and measurement. The switching
             product line allows Keithley to provide a complete measurement
             solution to customers in production test, semi-conductor
             characterization, and materials research applications.

             Sources generate the precise voltage and currents needed to test
             electronic devices and investigate properties of materials. Source
             products are sold to scientists and engineers in research,
             semiconductor and electronic manufacturing markets, especially
             where stable signals of low level current and voltage are needed.
             These sources can be interfaced with computers as part of an
             automated test system, or used manually on the laboratory bench.
             Switches and Sources are marketed primarily through personal
             selling.

                                       2
<PAGE>   5

             SOURCE MEASURE UNITS. These are programmable instruments capable of
             sourcing and measuring voltage, current and resistance, thus
             replacing the functionality of four instruments with one reliable,
             compact unit. These versatile instruments cover a wide dynamic
             range of voltage and current and their combination of high speed
             and resolution have made these units ideal for high volume
             production testing of electronic components for computers,
             automotive, and wireless communications products. The source
             measure units also provide the measurement sensitivity needed for
             materials research and semiconductor characterization applications.
             These products are marketed primarily through personal selling.

             PLUG-IN BOARDS. The qualities of these boards include data
             acquisition capabilities in the form of a board that is installed
             into a slot of the computer, boards that essentially contain an
             instrument allowing benchtop engineering and automatic production
             testing through an expansion slot of almost any personal computer,
             and IEEE-488 bus interfaces and software for interfacing computers
             with programmable measurement instrumentation. The boards are
             marketed worldwide to researchers and scientists engaged in
             laboratory automation and experimentation, engineers involved with
             process control and data collection applications, and machine
             builders and systems integrators involved in production test
             applications. These products are marketed primarily through direct
             marketing, catalog mailings, and personal selling.

             EXTERNAL SYSTEMS. These products include Keithley's MetraBus and
             SmartLink product offerings. Essentially, external systems are
             personal computer-based workstations that collect data from, and
             provide control over, a variety of test and measurement modules, as
             well as a line of intelligent measurement modules that allow
             laboratory-grade measurements virtually anywhere due to their small
             size. These products are primarily used in industrial monitoring
             and control applications, research, product test and pilot plant
             process monitoring. These products are marketed primarily through
             personal selling.

             ACCULEX. These products include digital panel meters and panel
             printers. They display machine parameters, capture results for
             permanent storage and enunciate alarms. These products are marketed
             primarily through direct marketing and catalog mailings.

             AGENCY PRODUCTS. The Company markets and distributes certain
             hardware and software products manufactured by several test and
             measurement companies. Software products are specialized personal
             computer-based scientific data acquisition, analysis and graphics
             software products. Scientists and engineers often combine the
             software together with data acquisition hardware or test and
             measurement instrumentation of Keithley or other manufacturers. The
             agency products are complementary to, but not competitive with,
             products manufactured by the Company.

         SEMICONDUCTOR. The Company's Semiconductor business unit designs,
develops, manufactures and markets automated parametric test systems and C-V
systems used by semiconductor manufacturers to measure various electrical
characteristics of semiconductor materials. These products are generally sold
through personal selling and can be found in semiconductor fabrication
facilities throughout the world. They consist of two main groups:

                                       3
<PAGE>   6

             APT PRODUCTS. The Company is one of the leading suppliers of these
             automated parametric test systems for semiconductor production
             applications. In production, the systems allow manufacturers to
             monitor quality control parameters during fabrication of integrated
             circuits to improve manufacturing yields. In research, the systems
             are used to analyze the characteristics of semiconductor materials
             in the development of integrated circuit devices. The systems can
             also be used to develop integrated circuit manufacturing processes.
             A typical system incorporates Keithley instrumentation and
             software, and computer hardware manufactured by others. The
             system's major components are integrated, and in most cases,
             customized to customer specification. The systems can also
             incorporate wafer test structures used for determining the
             reliability of semiconductor devices at various stages of
             manufacturing. These test structures allow the company's APT
             systems to determine the quality of both the wafer and the
             manufacturing process much earlier than with previous test methods.
             Installation and servicing of the equipment and software, and
             customer training are also provided. Selling prices for these
             products generally range from $100,000 to $350,000.

             C-V (CAPACITANCE VERSUS VOLTAGE). C-V systems include
             high-frequency and quasistatic C-V meters, measurement and analysis
             software, and computer-based test systems. C-V products are used by
             scientists and engineers in semiconductor development and
             manufacturing facilities, industrial and governmental research
             laboratories, and educational institutions to research, develop,
             and characterize semiconductor devices, materials and manufacturing
             processes.

NEW PRODUCTS DURING FISCAL YEAR 1998

         Several new products were introduced during fiscal 1998 including the
following:

         THE MODEL 2303 HIGH SPEED PRECISION POWER SUPPLY is optimized for
automated testing of portable wireless communication devices such as cellular
phones, cordless phones, pagers and mobile radios. Its fast response to load
changes is designed to simulate the current drive capacity of a battery. The
Model 2303 has features that allow easy verification of power consumption
specifications under different operating conditions. This is a valuable feature
for verifying performance of a cellular phone's standby mode, which requires the
processing of random-interval, control pulse transmissions from base stations.

         THE MODEL 2182 NANOVOLTMETER is designed for use in applications
requiring low voltage measurements. Priced lower than earlier models, it
eliminates the need for a computer controller when making precision I-V
measurements by providing the ability to control an external source. The Model
2182 is used by researchers, metrology labs and component test engineers.

         THE MODEL 2000-20 SCANNING MULTIMETER, designed for production test,
switch, and measure applications, is a 6 1/2-digit multimeter with a 20-channel
scanner card installed in its option slot that can be controlled from the front
panel or via the RS-232 or IEEE-488 interface. The Model 2000-20, with 20
channel switching, offers performance at approximately half the cost/channel of
a previous 10-channel system. The Model 2000-20 builds upon the standard 

                                       4

<PAGE>   7


Model 2000's high-performance, cost-effective design, combining a broad range of
functions with excellent accuracy specifications.

         THE KPCI-422/4R SERIAL INTERFACE BOARD permits the easy connection of
up to four standard RS-422A communication ports to a single short slot of a
PCI-equipped PC. The KPCI-422/4r is useful for applications requiring more
serial ports than are available in a standard PC, enabling serial communications
with multiple modems, printers, and terminals under Windows(R) 95/98/NT
operating systems. Easy to configure and use because of its true plug-and-play
capability, the KPCI-422/4r allows users to take advantage of the superior
performance of PCs equipped with a 32-bit PCI bus.


GEOGRAPHIC MARKETS AND DISTRIBUTION

         During fiscal 1998, all of the Company's products were manufactured in
Ohio and were sold throughout the world in many developed countries. The
Company's principal markets are the United States, Europe and the Pacific Basin.

         In the United States, the Company's products are sold by the Company's
sales personnel, independent sales representatives and through direct marketing
and catalog mailings. United States sales offices are located in Solon, Ohio    
and Santa Clara, California. The Company markets its products directly in 
countries in which it has a sales office and through distributors in other
countries. European subsidiaries have sales and service offices located in or
near London, Munich, Paris, Amsterdam, Zurich and Milan. The Company also has
sales offices in Belgium, China, Taiwan and India. Sales in markets outside the
above named locations are made through independent sales representatives and
distributors.

SOURCES AND AVAILABILITY OF RAW MATERIALS

         The Company's products require a wide variety of electronic and
mechanical components, most of which are purchased. The Company has multiple
sources for the vast majority of the components and materials it uses; however,
there are some instances where the components are obtained from a sole-source
supplier. If a sole-source supplier ceased to deliver, the Company could
experience a temporary adverse impact on its operations; however, management
believes alternative sources could be developed quickly. Although shortages of
purchased materials and components have been experienced from time to time,
these items have generally been available to the Company as needed.

PATENTS

         Electronic instruments of the nature the Company designs, develops and
manufactures cannot generally be patented in their entirety. Although the
Company holds patents with respect to certain of its products, it does not
believe that its business is dependent to any material extent upon any single
patent or group of patents, because of the rapid rate of technological change in
the industry.


                                       5
<PAGE>   8



SEASONAL TRENDS AND WORKING CAPITAL REQUIREMENTS

         Although the Company is not subject to significant seasonal trends, its
business is cyclical and is somewhat dependent upon the semiconductor industry
in particular. The Company does not have any unusual working capital
requirements.

CUSTOMERS

         The Company's customers generally are involved in engineering research
and development, product testing, electronic service or repair, and educational
and governmental research. During the fiscal year ended September 30, 1998 no
one customer accounted for more than 10% of the Company's sales. Management
believes that the loss of any one of its customers would not materially affect
the sales or net income of the Company.

BACKLOG

         The Company's backlog of unfilled orders amounted to approximately
$9,049,000 as of September 30, 1998 and approximately $13,486,000 as of
September 30, 1997. Included in the backlog at September 30, 1998 and 1997 is
$3,015,000 and $6,983,000, respectively, for Quantox products for which the
business was sold subsequent to September 30, 1998. It is expected that the
majority of the orders included in the 1998 backlog, except the Quantox
products, will be delivered during fiscal 1999; however, the Company's past
experience indicates that a small portion of orders included in the backlog may
be canceled.

COMPETITIVE CONDITIONS

         The Company competes on the basis of quality, performance, service,
warranty and price, with quality and performance frequently being dominant.
There are many firms in the world engaged in the manufacture of electronic
measurement instruments, some of which are larger and have greater financial
resources than the Company. The Company's competitors vary between product lines
and certain manufacturers compete with the Company in multiple product lines.
The Company's principal competitors are Hewlett-Packard Company and National
Instruments, Inc.


RESEARCH AND DEVELOPMENT

         The Company's engineering development activities are directed toward
the development of new products that will complement, replace or add to the
products currently included in the Company's product line. The Company does not
perform basic research, but on an ongoing basis utilizes new component and
software technologies in the development of its products. The highly technical
nature of the Company's products and the rapid rate of technological change in
the industry require a large and continuing commitment to engineering
development efforts. Product development expenses were $13,139,000 in 1998,
$17,233,000 in 1997 and $18,337,000 in 1996, or approximately 11%, 14% and 15%
of net sales, respectively, for each of the last three fiscal years.


                                       6
<PAGE>   9



GOVERNMENT REGULATIONS

         The Company believes that its current operations and its current uses
of property, plant and equipment conform in all material respects to applicable
laws and regulations. The Company has not experienced, nor does it anticipate,
any material claim or material capital expenditure in connection with
environmental laws and other regulations.

EMPLOYEES

         As of September 30, 1998, the Company employed 564 persons, 103 of whom
were located outside the United States. None of the Company's employees are
covered under the terms of a collective bargaining agreement and the Company
believes that relations with its employees are good.

FOREIGN OPERATIONS AND EXPORT SALES

         Information related to foreign and domestic operations and export sales
is contained in Note J of the Notes to the Consolidated Financial Statements on
page 30 of the Company's 1998 Annual Report to Shareholders, which page is
incorporated herein by reference.

         The Company has significant revenues from outside the United States
which increase the complexity and risk to the Company. These risks include
increased exposure to the risk of foreign currency fluctuations and the
potential economic and political impacts from conducting business in foreign
countries. With the exception of changes in the value of foreign currencies,
which is not possible to predict, the Company believes that its foreign
subsidiaries and other larger international markets are in countries where the
economic and political climate is generally stable.


                                       7
<PAGE>   10



ITEM 2 - PROPERTIES.

         The Company believes that the facilities owned and leased by it are
well maintained, adequately insured and suitable for their present and intended
uses. Pertinent information concerning the principal properties of the Company
and its subsidiaries is as follows:

<TABLE>
<CAPTION>

                           Type of                                                      Acreage (Land)
Owned Properties           Facility                                                Square Footage (Building)
----------------           --------                                                -------------------------
<S>                        <C>                                                     <C>
     Location

     Solon, Ohio           Executive offices,
                           Engineering, Manufacturing,                              26.1 Acres
                           Marketing and Sales                                      125,000 square feet

     Solon, Ohio           Engineering, Manufacturing,
                           Marketing, Sales, Service and                            7.0 Acres
                           Administration   76,000 square feet

     Solon, Ohio           This space is available for expansion.                   5.5 Acres
                           It is currently leased to other parties.                 50,000 square feet
</TABLE>

<TABLE>
<CAPTION>

                                                                                                 Lease
                           Type of                                         Square             Expiration
Leased Properties          Facility                                        Footage               Date
-----------------          --------                                        -------            ------------

     Location
     --------
<S>                        <C>                                             <C>             <C>
     Solon, Ohio           This space was occupied by the                     40,000        October 13, 2006
                           Radiation Measurements Division that was sold 
                           during 1998. The space is being sublet to the 
                           buyer; however, the Company remains responsible 
                           for the lease at the current time.

     Solon, Ohio           This space was used for manufacturing
                           and administration.  Currently, the
                           Company is not occupying any of the
                           space and plans to sublet it.                      21,600        March 31, 2002


     Santa Clara,          Sales and Service                                   4,355        October 13, 2002
     California
</TABLE>

                                       8
<PAGE>   11


<TABLE>
<CAPTION>
                                                                                             Lease
                           Type of                                    Square              Expiration
Location                   Facility                                  Footage                 Date
-----------------          --------                                  -------            ------------
<S>                        <C>                                        <C>            <C>
Munich,                    Sales, Service and                          27,750         March 31, 2001;
Germany                    Administration                                             renewable

London, England            Sales and Service                            5,600         July 24, 2009

Paris, France              Sales and Service                            3,456         June 30, 2004

Zurich,                    Sales and Service                            3,229         September 30, 1999
Switzerland                                                                           renewable

Amsterdam,                 Sales and Service                            2,906         March 31, 2002
Netherlands

Milan,                     Sales and Service                            2,691         August 31, 2001
Italy
</TABLE>


ITEM 3 - LEGAL PROCEEDINGS.
         -----------------

         The Company is not a party to any material litigation.

ITEM 4 - SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS.
         ---------------------------------------------------

         Not applicable.

                                       9
<PAGE>   12



EXECUTIVE OFFICERS OF THE REGISTRANT:
-------------------------------------

         The description of executive officers is included pursuant to
Instruction 3 to Section (b) of Item 401 of Regulation S-K under the Securities
and Exchange Act of 1934.

         The following table sets forth the names of all executive officers of
the Company and certain other information relating to their position held with
the Company and other business experience.

<TABLE>
<CAPTION>
Executive Officer                           Age         Recent Business Experience
-----------------                           ---         --------------------------
<S>                                        <C>          <C>
Joseph P. Keithley                           50         Chairman  of the  Board  of  Directors  since  1991,  Chief
                                                        Executive  Officer since November 1993 and President  since
                                                        May 1994.

Philip R. Etsler                             48         Vice President Human Resources of the Company since 1990.

James B. Griswold                            52         Secretary  and  a  Director  of  the  Company  since  1988;
                                                        partner in the law firm of Baker & Hostetler  LLP from 1982
                                                        to present.

David H. Patricy                             49         Vice  President  of Test  and  Measurement  of the  Company
                                                        since 1997.  Previously  General  Manager of the Instrument
                                                        Division  from 1994 to 1997 and  Director of  Manufacturing
                                                        from 1984 to 1994.

Mark J. Plush                                49         Vice President and Chief  Financial  Officer of the Company
                                                        since October 1998.  Previously,  Controller since 1982 and
                                                        an Officer of the Company since 1989.

Ronald M. Rebner (1)                         54         Vice President and Chief  Financial  Officer of the Company
                                                        from 1981 to October 1998.

Gabriel A. Rosica                            58         Senior  Vice  President  of  Semiconductor  since  February
                                                        1996.   Previously   Chief  Operating   Officer  of  Bailey
                                                        Controls  Company  from  August  1994 to  January  1996 and
                                                        Senior  Vice  President  of  Systems  Operations  of Bailey
                                                        Controls Company from January 1992 to July 1994.
</TABLE>


        (1) On October 1,1998, Mr. Rebner retired from his Executive Officer
position with the Company.

                                       10
<PAGE>   13



                                    PART II.

ITEM 5 - MARKET FOR THE REGISTRANT'S COMMON EQUITY AND RELATED         
         -----------------------------------------------------         
         STOCKHOLDER MATTERS.
         --------------------


         See the table under the caption Stock Market Price and Cash Dividends
appearing on page 33 of the Keithley Instruments, Inc. 1998 Annual Report to
Shareholders, which table and information are incorporated herein by this
reference.

         The approximate number of shareholders of record of Common Shares and
Class B Common Shares, including those shareholders participating in the
Dividend Reinvestment Plan, as of December 15, 1998 was 2,460.

ITEM 6 - SELECTED FINANCIAL DATA.
         -------------------------

         See the eleven year summary, appearing on pages 34 and 35 of the
Keithley Instruments, Inc. 1998 Annual Report to Shareholders, which pages are
incorporated herein by this reference.

ITEM 7 - MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL    
         -------------------------------------------------
         CONDITION AND RESULTS OF OPERATIONS.
         -----------------------------------

         See pages 19 through 21 of the Keithley Instruments, Inc. 1998 Annual
Report to Shareholders, which pages are incorporated herein by this reference.

ITEM 8 - FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA.
         --------------------------------------------

         See pages 16 through 18, pages 22 through 31, and page 33 of the
Keithley Instruments, Inc. 1998 Annual Report to Shareholders, together with the
report thereon of PricewaterhouseCoopers LLP dated November 23, 1998, appearing
on page 32 of the Keithley Instruments, Inc. 1998 Annual Report to Shareholders,
which pages are incorporated herein by this reference.

ITEM 9 - CHANGES IN AND DISAGREEMENTS WITH ACCOUNTANTS ON     
         ------------------------------------------------
         ACCOUNTING AND FINANCIAL DISCLOSURE.
         ------------------------------------

         None.

                                       11
<PAGE>   14



                                    PART III.

ITEM 10 - DIRECTORS AND EXECUTIVE OFFICERS OF THE REGISTRANT.
         ---------------------------------------------------- 
         See the table listing the nominees for directors under the caption
"Election of Directors" in the Company's Proxy Statement to be used in
conjunction with the February 13, 1999 Annual Meeting of Shareholders and filed
with the Securities and Exchange Commission pursuant to Section 14(a) of the
Securities Exchange Act of 1934, which table is incorporated herein by this
reference. The information required for an identification of executive officers
is included on page 10 of this Form 10-K Annual Report.

ITEM 11 - EXECUTIVE COMPENSATION.
          ------------------------
         See the caption "Executive Compensation and Benefits" in the Company's
Proxy Statement to be used in conjunction with the February 13, 1999 Annual
Meeting of Shareholders and filed with the Securities and Exchange Commission
pursuant to Section 14(a) of the Securities Exchange Act of 1934, which section
is incorporated herein by this reference.

ITEM 12 - SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND MANAGEMENT.
          ---------------------------------------------------------------
         See the caption "Principal Shareholders" in the Company's Proxy
Statement to be used in conjunction with the February 13, 1999 Annual Meeting of
Shareholders and filed with the Securities and Exchange Commission pursuant to
Section 14(a) of the Securities Exchange Act of 1934, which section is
incorporated herein by this reference.

ITEM 13 - CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS.
          -----------------------------------------------
         James B. Griswold, a Director and nominee for Director, is a partner in
the law firm of Baker & Hostetler LLP. Baker & Hostetler LLP served as general
legal counsel to the Company during the fiscal year ended September 30, 1998,
and is expected to render services in such capacity to the Company in the
future.


                                       12
<PAGE>   15



                                    PART IV.

ITEM 14 - EXHIBITS, FINANCIAL STATEMENT SCHEDULES AND REPORTS ON FORM 8-K.
          ----------------------------------------------------------------

(A)(1)  FINANCIAL STATEMENTS OF THE COMPANY

         The following documents included in the Keithley Instruments, Inc. 1998
Annual Report to Shareholders, are incorporated herein by reference:

1.       Consolidated Balance Sheet as of September 30, 1998 and 1997.

2.       Consolidated Statement of Income for the years ended September 30,
         1998, 1997 and 1996.

3.       Consolidated Statement of Cash Flows for the years ended September 30,
         1998, 1997 and 1996.

4.       Consolidated Statement of Shareholders' Equity for the years ended
         September 30, 1998, 1997 and 1996.

5.       Notes to Consolidated Financial Statements.

6.       Report of Independent Accountants dated November 23, 1998.

(A)(2)  FINANCIAL STATEMENT SCHEDULES

The following additional information should be read in conjunction with the
Consolidated Financial Statements of the Company described in Item 14(a)(1):

Schedule II  Valuation and Qualifying Accounts

Schedules other than those listed above are omitted because they are not
required or not applicable, or because the information is furnished elsewhere in
the consolidated financial statements or the notes thereto.

                                       13
<PAGE>   16



<TABLE>
<CAPTION>
(A)(3)  INDEX TO EXHIBITS

                                                                                                            Page Number
                                                                                                            Sequential
          Exhibit                                                                                            Numbering
          Number                  Exhibit                                                                     System
          ------                  -------                                                                     ------
<S>                     <C>                                                                                <C>
          2(a)          Asset Purchase Agreement by and between Keithley
                        Instruments, Inc. and Inovision Radiation Measurements,
                        LLC dated July 31, 1998. (Reference is made to Exhibit
                        2(a) of the Company's Current Report on Form 8-K dated
                        July 31, 1998 (File No. 1-9965), which Exhibit is
                        incorporated herein by reference.)
                                                                                                                 --
          3(a)          Amended Articles of Incorporation, as amended on
                        February 11, 1985. (Reference is made to Exhibit 3(a) of
                        the Company's Form 10 Registration Statement (File No.
                        0-13648) as declared effective on July 31, 1985, which
                        Exhibit is incorporated herein by reference.)
                                                                                                                 --
          3(b)          Code of Regulations, as amended on February 11, 1985.  
                        (Reference is made to Exhibit 3(b) of the Company's
                        Form 10 Registration Statement (File No. 0-13648) as
                        declared effective on July 31, 1985, which Exhibit is
                        incorporated herein by reference.)                                                       --

          3(c)          Amended Articles of Incorporation, as amended on
                        February 10, 1996. (Reference is made to Exhibit 3(c)
                        of the Company's Quarterly Report on Form 10-Q for
                        the fiscal quarter ended March 31, 1996 (File No.
                        1-9965), which Exhibit is incorporated herein by
                        reference.)                                                                              --

          4(a)          Specimen Share Certificate for the Common Shares,
                        without par value. (Reference is made to Exhibit 4(a)
                        of the Company's Quarterly Report on Form 10-Q for
                        the fiscal quarter ended June 30, 1988 (File No.
                        1-9965), which Exhibit is incorporated herein by
                        reference.)                                                                              --

          4(b)          Specimen Share Certificate for the Class B Common
                        Shares, without par value. (Reference is made to
                        Exhibit 4(b) of the Company's Form 10 Registration
                        Statement (File No. 0-13648) as declared effective on
                        July 31, 1985, which Exhibit is incorporated herein
                        by reference.)                                                                           --

          *10(a)        1984 Stock Option Plan, adopted in February 1984.                                        --

          *10(c)        1984 Deferred Compensation Plan, adopted in February 1984.                               --

                        *Reference is made to the appropriate Exhibits of the
                        Company's Form 10 Registration Statement (File No.
                        0-13648) as declared effected on July 31, 1985, which
                        Exhibits are incorporated herein by reference.
</TABLE>

                                       14
<PAGE>   17


<TABLE>
<CAPTION>
                                                                                                            Page Number
                                                                                                            Sequential
          Exhibit                                                                                            Numbering
          Number                  Exhibit                                                                     System
          ------                  -------                                                                     ------
<S>                     <C>                                                                                 <C>
          10(k)         Employment Agreement with Mark J. Plush dated April 7, 1994.                           22 - 27

          10(l)         Employment Agreement with Joseph P. Keithley dated
                        September 26, 1988. (Reference is made to Exhibit 10(l)
                        of the Company's Annual Report on Form 10-K for the year
                        ended September 30, 1988 (File No. 1-9965), which
                        Exhibit is incorporated herein by reference.)
                                                                                                                 --

          10(o)         Form of Supplemental Executive Retirement Plan, adopted
                        in January 1988. (Reference is made to Exhibit 10(o) of
                        the Company's Annual Report on Form 10-K for the year
                        ended September 30, 1988 (File No. 1-9965), which
                        Exhibit is incorporated herein by reference.)
                                                                                                                 --
          10(q)         1992 Stock Incentive Plan, adopted in December 1991.
                        (Reference is made to Exhibit 10(q) of the Company's
                        Annual Report on form 10-K for the year ended
                        September 30, 1991 (File No. 1-9965) which Exhibit is
                        incorporated herein by reference.)                                                       --

          10(r)         1992 Directors' Stock Option Plan, adopted in
                        December 1991. (Reference is made to Exhibit 10(r) of
                        the Company's Annual Report on form 10-K for the year
                        ended September 30, 1991 (File No. 1-9965) which
                        Exhibit is incorporated herein by reference.)                                            --

          10(u)         Credit Agreement dated as of May 31, 1994 by and among
                        Keithley Instruments, Inc. and certain borrowing
                        subsidiaries and the Banks named herein, and NBD Bank,
                        N.A., as Agent. (Reference is made to Exhibit 10(u) of
                        the Company's Quarterly Report on form 10-Q for the
                        quarter ended June 30, 1994 (File No. 1-9965) which
                        Exhibit is incorporated herein by reference.)
                                                                                                                 --
          10(x)         1996 Outside Directors Deferred Stock Plan.
                        (Reference is made to Exhibit 10(x) of the Company's
                        Quarterly Report on Form 10-Q for the fiscal quarter
                        ended March 31, 1996 (File No. 1-9965), which Exhibit
                        is incorporated herein by reference.)                                                    --
</TABLE>


                                       15
<PAGE>   18



<TABLE>
<CAPTION>
                                                                                                            Page Number
                                                                                                            Sequential
          Exhibit                                                                                            Numbering
          Number                  Exhibit                                                                     System
          ------                  -------                                                                     ------
<S>       <C>                                                                                          <C>
          10(y)         First Amendment dated March 28, 1997, to the Credit
                        Agreement dated May 31, 1994. (Reference is made to
                        Exhibit 10(y) of the Company's Quarterly Report on Form
                        10-Q for the fiscal quarter ended March 31, 1997 (File
                        No. 1-9965), which Exhibit is incorporated herein by
                        reference.)
                                                                                                                 --
          10(z)         1997 Directors' Stock Option Plan, adopted in February
                        1997. (Reference is made to Exhibit 10(z) of the
                        Company's Annual Report on form 10-K for the fiscal year
                        ended September 30, 1997 (File No. 1-9965), which
                        Exhibit is incorporated herein by reference.)
                                                                                                                 --

          11            Statement Re Computation of Per Share Earnings.                                          28

          13            Annual Report to Shareholders for the Fiscal Year Ended 
                        September 30, 1998.                                                                     29-67
                                                                                                                
          21            Subsidiaries of the Company.                                                             68

          23            Consent of Experts.                                                                      69

          27            Financial Data Schedule (EDGAR version only).                                            --
</TABLE>


ITEM 14(B)  REPORTS ON FORM 8-K.

During the fourth quarter ended September 30, 1998, the Company filed a Current
Report on Form 8-K under Item 2 - Acquisition or Disposition of Assets for the
sale of certain assets of its Radiation Measurements Division. The Form 8-K,
dated July 31, 1998, included an Unaudited Pro forma Consolidated Balance Sheet
as of June 30, 1998, Unaudited Pro forma Consolidated Statements of Income for
the fiscal year ended September 30, 1997 and the nine months ended June 30,
1998, and Notes thereto.

ITEM 14(C)  EXHIBITS:  See "Index to Exhibits" at Item 14(a)(3) above.

ITEM 14(D) FINANCIAL STATEMENT SCHEDULES: Schedules required to be filed in
response to this portion of Item 14 are listed above in Item 14(a)(2).

                                       16
<PAGE>   19



                                   SIGNATURES

         Pursuant to the requirements of Section 13 or 15(d) of the Securities
Exchange Act of 1934, the Registrant has duly caused this report to be signed on
its behalf by the undersigned, thereunto duly authorized.

Keithley Instruments, Inc.
(Registrant)

By:   /s/  Joseph P. Keithley
   --------------------------------------------
           Joseph P. Keithley, (Chairman, President and Chief Executive Officer)

Date:   December 21, 1998
     ------------------------------------------

         Pursuant to the requirements of the Securities Exchange Act of 1934,
this report has been signed below by the following persons on behalf of the
Registrant and in the capacities on the date indicated.

<TABLE>
<CAPTION>
Signature                                      Title                                                       Date
---------                                      -----                                                       ----
<S>                                            <C>                                                      <C>
/s/  Joseph P. Keithley                        Chairman of the Board of Directors,                       12/21/98
--------------------------------------------   President and Chief Executive Officer
     Joseph P. Keithley                        (Principal Executive Officer)

/s/  Brian R. Bachman                          Director                                                  12/21/98
-------------------------------------------
     Brian R. Bachman

/s/  James T. Bartlett                         Director                                                  12/21/98
-------------------------------------------
     James T. Bartlett

/s/  Arden L. Bement, Jr.                      Director                                                  12/21/98
-------------------------------------------
     Dr. Arden L. Bement, Jr.

/s/  James B. Griswold                         Director                                                  12/21/98
-------------------------------------------
     James B. Griswold

/s/  Leon J. Hendrix, Jr.                      Director                                                  12/21/98
-------------------------------------------
     Leon J. Hendrix, Jr.

/s/  R. Elton White                            Director                                                  12/21/98
-------------------------------------------
     R. Elton White
</TABLE>


                                       17

<PAGE>   20



Report of Independent Accountants on
Financial Statement Schedule



To the Board of Directors of
Keithley Instruments, Inc.


Our audits of the consolidated financial statements referred to in our report
dated November 23, 1998 appearing on page 32 of the 1998 Annual Report to
Shareholders of Keithley Instruments, Inc., (which report and consolidated
financial statements are incorporated by reference in this Annual Report on Form
10-K) also included an audit of the Financial Statement Schedule listed in Item
14(a)(2) of this Form 10-K. In our opinion, this Financial Statement Schedule
presents fairly, in all material respects, the information set forth therein
when read in conjunction with the related consolidated financial statements.




PricewaterhouseCoopers LLP

Cleveland, Ohio
November 23, 1998


                                       18
<PAGE>   21



                                                                     SCHEDULE II

                           KEITHLEY INSTRUMENTS, INC.
                        VALUATION AND QUALIFYING ACCOUNTS
                            (In Thousands of Dollars)




<TABLE>
<CAPTION>
Column A                               Column B               Column C              Column D               Column E
--------                               --------               --------              --------               --------
                                      Balance at          
                                     Beginning of         Charged to Costs                              Balance at End
Description                            Period               and Expenses         Deductions (1)            of Period
-----------                            ------               ------------         --------------            ---------
<S>                                 <C>                   <C>                   <C>                     <C>
For the Year Ended 
September 30, 1998:

Valuation allowance for
deferred tax assets                     $3,166                  $ 54                  $ 93                  $3,127

For the Year Ended September
30, 1997:

Valuation allowance for
deferred tax assets                     $2,994                  $172                   --                   $3,166

For the Year Ended 
September 30, 1996:

Valuation allowance for
deferred tax assets                     $2,606                  $467                  $ 79                  $2,994
</TABLE>


(1) Represents utilization of tax credits and capital loss carryovers.

                                       19