<PAGE>   1
                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                  FORM 10-K/A2

(Mark One)

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

        For the fiscal year ended September 30, 1998

                                       OR

   [ ]  TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d)
        OF THE SECURITIES EXCHANGE ACT OF 1934

        For the transition period from _________ to _________.

        Commission File Number 1-6805.
                                 -----------------------------

                        BROWNING-FERRIS INDUSTRIES, INC.
             (Exact name of registrant as specified in its charter)

         DELAWARE                                              74-1673682
(State or other jurisdiction of                             (I.R.S. Employer
incorporation or organization)                             Identification No.)

         757 N. ELDRIDGE
           HOUSTON, TEXAS                                         77079
(Address of principal executive offices)                         (Zip Code)

Registrant's telephone number, including area code: (281) 870-8100.



<PAGE>   2



                                    PART III.

ITEM 10. DIRECTORS AND EXECUTIVE OFFICERS OF THE REGISTRANT.

    Information required with respect to executive officers of the Company is
set forth under "Business - Executive Officers of the Company" in Part I of this
report.

    The directors of the Company, their positions and offices, their respective
term of office as a director and their respective ages are as follows:

<TABLE>
<CAPTION>
                                                                             EXPIRATION
                             POSITIONS AND OFFICES      SERVED AS A          OF PRESENT
         NAME                  WITH THE COMPANY       DIRECTOR SINCE  AGE*      TERM
-------------------------- -------------------------  --------------  ----   ----------
<S>                        <C>                        <C>            <C>     <C>
William D. Ruckelshaus.... Chairman of the Board and       1987        66       1999
                           Director(1)
Bruce E. Ranck............ President, Chief                1990        50       1999
                           Executive
                           Officer and Director(1)
John W. Alden............. Director(3)(8)                  1998        57       2001
Gregory D. Brenneman...... Director(2)(4)(6)               1997        37       2000
William T. Butler......... Director(1)(3)                  1990        66       2001
Gerald Grinstein.......... Director(3)(5)(6)               1990        66       1999
Robert J. Herbold......... Director(4)(8)                  1998        56       2001
Harry J. Phillips, Sr..... Director(1)                     1970        68       2000
Joseph L. Roberts, Jr..... Director(2)                     1991        63       2001
Marc J. Shapiro........... Director(4)(5)(7)               1994        51       2000
Robert M. Teeter.......... Director(2)(5)(6)(8)            1989        59       2000
Marina v.N. Whitman....... Director(3)(4)                  1992        63       2001
</TABLE>

----------

*   As of January 11, 1999.

(1) Member of the Executive Committee

(2) Member of the Corporate Responsibility Committee

(3) Member of the Compensation Committee

(4) Member of the Audit Committee

(5) Member of the Directors and Corporate Governance Committee

(6) Member of the Strategic Industry Development Committee

(7) Advisory Member of the Strategic Industry Development Committee

(8) Member of the Marketing Committee


                                       2
<PAGE>   3


Background of Directors

    Mr. Ruckelshaus was elected a director in June 1987 and Chairman of the
Board and Chief Executive Officer in September 1988. He stepped down as the
Company's Chief Executive Officer in October 1995, but remains as Chairman of
the Board. Mr. Ruckelshaus also serves as a director of Cummins Engine Company,
Monsanto Company, Nordstrom, Inc., Weyerhaeuser Company, Solutia Inc., Coinstar,
Inc. and Gargoyles Inc.

    Mr. Ranck was elected President and Chief Executive Officer in October 1995,
having served as President and Chief Operating Officer of the Company since
November 1991 and as Executive Vice President (Solid Waste Operations -- North
America) from October 1989 until November 1991. Prior to that time, he served as
a Regional Vice President in one of the Company's former regions. He also serves
as a director of Furon Company.

    Mr. Alden serves as Vice Chairman of United Parcel Service (UPS), a position
he has held since November 1996. He previously held the office of Senior Vice
President of Business Development, a position he held from 1986. He has served
as a director of UPS since 1988. He joined UPS in 1965 and spent the majority of
his career in customer service and sales positions prior to being named National
Customer Development Manager in 1978. He is a director of Unistar Air Cargo, the
joint venture between UPS and Yamoto Transport of Japan to market cargo services
for the U.S. - Japan trading lane.

    Mr. Brenneman is currently President and Chief Operating Officer of
Continental Airlines, Inc., a position he has held since April 1995. He also
serves as a director of Continental Airlines, Inc. and as Vice Chairman of
Continental Micronesia and Continental Express. Mr. Brenneman also serves as a
director of J. Crew Group, Inc. From 1993 until he joined Continental Airlines
in 1995, he was a partner in Bain & Company, Inc., a consulting firm, where he
specialized in corporate turnarounds.

    Dr. Butler serves as Chancellor of Baylor College of Medicine in Houston,
Texas, where he previously served as President and Chief Executive Officer from
1979 until January 1996. He is also the past Chairman of the Association of
American Medical Colleges. Dr. Butler also serves as a director of C.R. Bard,
Inc. and Chairman of the Board of Lyondell Petrochemical Company.

    Mr. Grinstein currently serves as Chairman of the Board of Delta Air Lines.
He also serves as a director of Sundstrand Corporation, Imperial Holly
Corporation, PACCAR Inc. and Vans, Inc. Mr. Grinstein served as Chairman, Chief
Executive Officer, President and a director of Burlington Northern Santa Fe
Corporation and Burlington Northern Railroad Company from 1989 until his
retirement in December 1995.

    Mr. Herbold has served as Executive Vice President and Chief Operating
Officer of Microsoft Corporation since November 1994 and serves on its Executive
Committee. He served as Senior Vice President, Advertising and Information
Services, at The Procter & Gamble Company, a position held from 1990 until his
joining Microsoft in 1994.

    Mr. Phillips served as Chairman of the Board and Chief Executive Officer of
the Company from September 1980 until September 1988, when he was elected
Chairman of the Executive Committee. Mr. Phillips is a director of RFS Hotel
Investors, Inc., Buckeye Technologies, Inc., Buckman Laboratories, Morgan Keegan
Inc. and the National Commerce Bancorporation, Memphis, Tennessee.

    Dr. Roberts has served as Senior Pastor of the Ebenezer Baptist Church in
Atlanta, Georgia since 1975.

    Mr. Shapiro currently serves as Vice Chairman, Finance and Risk Management
of The Chase Manhattan Bank. From 1989 until assuming his current role in
September 1997, he was Chairman, President and Chief Executive Officer of Texas
Commerce Bank National Association, a subsidiary of The Chase Manhattan
Corporation. He also serves as a director of Weingarten Realty Investors and
Burlington Northern Santa Fe Corporation.

    Mr. Teeter has served as President of Coldwater Corporation, a strategic
planning and public affairs consulting firm since 1988. He is also a director of
United Parcel Service, Bank of Ann Arbor, Durakon Industries, Inc. and Optical
Imagine Systems.

    Dr. Whitman has served as Professor of Business Administration and Public
Policy at the University of Michigan since 1992. Previously, she spent thirteen
years at General Motors Corporation, six years as Vice President and Chief
Economist and seven years as Vice President and Group Executive, Public Affairs
Staffs. She currently serves as a director of The Procter & Gamble Company, The
Chase Manhattan Corporation, Alcoa Corporation and UNOCAL Corporation.


                                       3
<PAGE>   4

SECTION 16(a) BENEFICIAL OWNERSHIP REPORTING COMPLIANCE.

    Based solely upon a review of Forms 3 and 4 furnished to the Company during
its most recent fiscal year and Forms 5 furnished to the Company with respect to
its most recent fiscal year, the Company believes that all transactions by
reporting persons were reported on a timely basis.


                                   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.


                                       BROWNING-FERRIS INDUSTRIES, INC.
                                                 (Registrant)


DATE: June 14, 1999           By:                 /s/ Bruce E. Ranck
                                    --------------------------------------------
                                                    Bruce E. Ranck
                                              President, Chief Executive
                                                 Officer and Director


                                       4