<PAGE>   1
================================================================================


                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549



                                    FORM 10-Q

                  (MARK ONE)
         [X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE
             SECURITIES EXCHANGE ACT OF 1934

             FOR THE QUARTERLY PERIOD ENDED MARCH 31, 2000 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 1-9215


                     ---------------------------------------


                       UNITED ASSET MANAGEMENT CORPORATION
             (Exact name of registrant as specified in its charter)

                DELAWARE                                04-2714625
     (State or other jurisdiction of     (I.R.S. Employer Identification Number)
     incorporation or organization)

                             ONE INTERNATIONAL PLACE
                           BOSTON, MASSACHUSETTS 02110
                    (Address of principal executive offices)

       Registrant's telephone number, including area code: (617) 330-8900

       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 (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days. [X] Yes [ ] No

       The number of shares outstanding of the registrant's common stock as of
May 5, 2000 was 56,491,561.


================================================================================
<PAGE>   2

                                     PART I
                              FINANCIAL INFORMATION


Item 1.       Financial Statements. (Pages F-1 to F-6)

Item 2.       Management's Discussion and Analysis of Financial Condition and
              Results of Operations. (Pages F-6 to F-8)

Item 3.       Quantitative and Qualitative Disclosures About Market Risk.
              (Page F-9)


                                     PART II
                                OTHER INFORMATION

Item 1.       Legal Proceedings.
              The Company and certain of the Company's subsidiaries are subject
              to legal proceedings arising in the ordinary course of business.
              On the basis of information presently available and advice
              received from legal counsel, it is the opinion of management that
              the disposition or ultimate determination of such legal
              proceedings will not have a material adverse effect on the
              Company's consolidated financial position, its consolidated
              results of operations or its consolidated cash flows.

Item 2.       Changes in Securities.
              During the first quarter of 2000, UAM issued an aggregate of
              125,455 shares of its Common Stock upon the exercise of warrants.
              This issuance was exempt from registration under Section 4(2) of
              the Securities Act of 1933. UAM had originally issued the warrants
              as consideration for its acquisitions of certain of its
              subsidiaries. The exercise price of the warrants was $16.50 per
              share.

Item 3.       Defaults Upon Senior Securities.  None

Item 4.       Submission of Matters to a Vote of Security Holders.  None

Item 5.       Other Information.  None

Item 6.       Exhibits and Reports on Form 8-K.

              (a)     Exhibit 3 - Amended and Restated By-laws of the Registrant
                      (effective as of March 29, 2000)

                      Exhibit 10 - United Asset Management Corporation Profit
                          Sharing and 401(k) Plan, Sixth Amendment

                      Exhibit 11 - Calculation of Earnings Per Share (Page F-10)

                      Exhibit 27 - Financial Data Schedule

              (b)     There have been no reports on Form 8-K filed by the
                      Company during the quarter ended March 31, 2000.

<PAGE>   3

         Pursuant to the requirements 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.

                                           UNITED ASSET MANAGEMENT CORPORATION

MAY 5, 2000                               /s/  William H. Park
-------------------------                  --------------------------------
(Date)                                     William H. Park
                                           Executive Vice President and
                                           Chief Financial Officer


<PAGE>   4

                          PART I. FINANCIAL INFORMATION

ITEM 1.   FINANCIAL STATEMENTS


                       UNITED ASSET MANAGEMENT CORPORATION

                      CONSOLIDATED STATEMENT OF OPERATIONS
                                   (Unaudited)

<TABLE>
<CAPTION>

-------------------------------------------------------------------------------------------------------------
Three Months Ended March 31,                                         2000                           1999
-------------------------------------------------------------------------------------------------------------
<S>                                                              <C>                            <C>
Revenues                                                         $239,048,000                   $217,695,000
-------------------------------------------------------------------------------------------------------------
Operating expenses:
     Compensation and related
        expenses                                                  125,075,000                    109,069,000
     Amortization of cost assigned
        to contracts acquired                                      26,294,000                     26,088,000
     Other operating expenses                                      38,248,000                     39,146,000
-------------------------------------------------------------------------------------------------------------
                                                                  189,617,000                    174,303,000
-------------------------------------------------------------------------------------------------------------
Operating income                                                   49,431,000                     43,392,000
-------------------------------------------------------------------------------------------------------------
Non-operating expenses:
     Interest expense, net                                         16,789,000                     15,834,000
     Other amortization                                             1,139,000                      1,159,000
-------------------------------------------------------------------------------------------------------------
                                                                   17,928,000                     16,993,000
-------------------------------------------------------------------------------------------------------------
Income before income tax expense                                   31,503,000                     26,399,000
Income tax expense                                                 13,042,000                     11,298,000
-------------------------------------------------------------------------------------------------------------
Net income                                                       $ 18,461,000                   $ 15,101,000
=============================================================================================================
Basic earnings per share                                                 $.33                           $.25
Diluted earnings per share                                               $.33                           $.25
Dividends declared per share                                             $.20                           $.20
=============================================================================================================
</TABLE>

See Notes to Condensed Consolidated Financial Statements.



                                      F-1
<PAGE>   5

                       UNITED ASSET MANAGEMENT CORPORATION

                      CONDENSED CONSOLIDATED BALANCE SHEET
<TABLE>
<CAPTION>

---------------------------------------------------------------------------------------------------------------------------
                                                                                 March 31,                    December 31,
                                                                                   2000                           1999
                                                                                (Unaudited)
---------------------------------------------------------------------------------------------------------------------------
<S>                                                                            <C>                           <C>
Assets
Current assets:
     Cash and cash equivalents                                                $  147,369,000                $  123,754,000
     Investment advisory fees receivable                                         175,244,000                   169,566,000
     Other current assets                                                         12,437,000                    11,621,000
---------------------------------------------------------------------------------------------------------------------------
Total current assets                                                             335,050,000                   304,941,000
Fixed assets, net                                                                 35,406,000                    37,391,000
Cost assigned to contracts acquired, net                                         815,127,000                   841,454,000
Other assets                                                                     141,353,000                   137,905,000
---------------------------------------------------------------------------------------------------------------------------
Total assets                                                                  $1,326,936,000                $1,321,691,000
===========================================================================================================================
Liabilities and Stockholders' Equity
Current liabilities:
     Accounts payable and accrued expenses                                    $  123,403,000                $  134,556,000
     Accrued compensation                                                         78,831,000                    87,994,000
---------------------------------------------------------------------------------------------------------------------------
Total current liabilities                                                        202,234,000                   222,550,000
Senior notes payable                                                             736,622,000                   700,401,000
Subordinated notes payable                                                       179,886,000                   181,737,000
Deferred income taxes and other                                                   27,654,000                    31,883,000
---------------------------------------------------------------------------------------------------------------------------
Total liabilities                                                              1,146,396,000                 1,136,571,000
---------------------------------------------------------------------------------------------------------------------------
Commitments and contingencies
Stockholders' equity:
     Common stock, par value $.01 per share                                          690,000                       703,000
     Capital in excess of par value                                              354,855,000                   361,808,000
     Retained earnings                                                           127,174,000                   139,044,000
     Accumulated other comprehensive income                                       (7,179,000)                   (6,495,000)
---------------------------------------------------------------------------------------------------------------------------
                                                                                 475,540,000                   495,060,000
     Less treasury shares at cost                                               (295,000,000)                 (309,940,000)
---------------------------------------------------------------------------------------------------------------------------
Total stockholders' equity                                                       180,540,000                   185,120,000
---------------------------------------------------------------------------------------------------------------------------
Total liabilities and stockholders' equity                                    $1,326,936,000                $1,321,691,000
===========================================================================================================================
</TABLE>

See Notes to Condensed Consolidated Financial Statements.



                                      F-2
<PAGE>   6


                       UNITED ASSET MANAGEMENT CORPORATION

                 CONDENSED CONSOLIDATED STATEMENT OF CASH FLOWS
                                   (Unaudited)

<TABLE>
<CAPTION>
----------------------------------------------------------------------------------------------------------------
Three Months Ended March 31,                                                  2000                     1999
----------------------------------------------------------------------------------------------------------------
<S>                                                                       <C>                      <C>
Cash flow related to operating activities:
     Net income                                                           $ 18,461,000             $ 15,101,000
     Adjustments to reconcile net income to net cash flow
        from operating activities:
        Amortization of cost assigned to contracts acquired                 26,294,000               26,088,000
        Depreciation                                                         3,481,000                3,618,000
        Amortization of goodwill and other                                   2,075,000                1,968,000
----------------------------------------------------------------------------------------------------------------
     Net income plus amortization and depreciation                          50,311,000               46,775,000
     Changes in assets and liabilities:
        Decrease (increase) in investment advisory fees receivable          (5,851,000)              13,401,000
        Increase in other current assets                                      (835,000)              (1,445,000)
        Decrease in accounts payable and accrued expenses                  (10,808,000)             (24,243,000)
        Decrease in accrued compensation                                    (9,128,000)             (28,031,000)
        Increase (decrease) in deferred income taxes and other              (5,035,000)                 474,000
----------------------------------------------------------------------------------------------------------------
Net cash flow from operating activities                                     18,654,000                6,931,000
----------------------------------------------------------------------------------------------------------------
Cash flow related to investing activities:
     Cash additions to cost assigned to contracts acquired                           -               (4,997,000)
     Change in other assets                                                 (6,236,000)              (3,785,000)
----------------------------------------------------------------------------------------------------------------
Net cash flow used in investing activities                                  (6,236,000)              (8,782,000)
----------------------------------------------------------------------------------------------------------------
Cash flow related to financing activities:
     Purchase of treasury shares                                           (13,149,000)             (71,159,000)
     Additions to notes payable, net                                        35,393,000               47,329,000
     Issuance or reissuance of equity securities                               844,000               11,274,000
     Dividends paid                                                        (11,459,000)             (12,290,000)
----------------------------------------------------------------------------------------------------------------
Net cash flow from (used in) financing activities                           11,629,000              (24,846,000)
----------------------------------------------------------------------------------------------------------------
Effect of foreign exchange rate changes on cash flow                          (432,000)                (850,000)
----------------------------------------------------------------------------------------------------------------
Net increase (decrease) in cash and cash equivalents                        23,615,000              (27,547,000)
Cash and cash equivalents at beginning of quarter                          123,754,000              153,616,000
----------------------------------------------------------------------------------------------------------------
Cash and cash equivalents at end of quarter                               $147,369,000             $126,069,000
================================================================================================================
</TABLE>














See Notes to Condensed Consolidated Financial Statements.


                                      F-3
<PAGE>   7


                       UNITED ASSET MANAGEMENT CORPORATION

              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS
                                   (Unaudited)


Note 1

         In the opinion of management, the accompanying unaudited Condensed
Consolidated Financial Statements contain all adjustments, consisting only of
normal recurring accruals, necessary to present fairly the financial position of
the Company and its subsidiaries at March 31, 2000, and their results of
operations and cash flows for the three months ended March 31, 2000 and 1999.
These Financial Statements should be read in conjunction with the Company's
Annual Report on Form 10-K for the year ended December 31, 1999.

Note 2

         Accumulated depreciation of fixed assets was $64,946,000 and
$62,997,000 at March 31, 2000 and December 31, 1999, respectively. The
accumulated amortization of cost assigned to contracts acquired was $717,280,000
and $700,410,000 at March 31, 2000 and December 31, 1999, respectively.

Note 3

         The Company has a program to repurchase shares of its common stock to
meet the requirements for future issuance of shares upon the exercise of stock
options and warrants. During the three-month period ended March 31, 2000, the
Company repurchased 815,300 shares of its common stock at a cost of $13,149,000.
In addition, exercises of warrants resulted in the Company extinguishing
subordinated notes, receiving cash and issuing stock as follows:

                                                            Three Months
                                                                Ended
                                                          March 31, 2000
                                                          --------------

          Subordinated notes extinguished                  $ 1,245,000
          Cash received                                    $   825,000
          Treasury shares reissued                             125,455


         As of March 31, 2000, the Company held 12,500,571 treasury shares.
Warrants for the purchase of 7,173,000 shares and stock options for the purchase
of 9,845,000 shares were outstanding at weighted average exercise prices of
$24.61 and $21.01, respectively.

         During the three-month period ending March 31, 2000, the Company
retired 1,354,445 shares of treasury stock, which had a total cost of
$24,326,000 and resulted in a charge to capital in excess of par value and
retained earnings of $6,972,000 and $17,340,000, respectively.


                                      F-4
<PAGE>   8

Note 4

         The components of comprehensive income for the three months ended March
31, 2000 and 1999, respectively, are set forth below:

                                                     Three Months Ended
                                                     ------------------
                                             March 31, 2000      March 31, 1999
                                             --------------      --------------

        Net income                              $18,461,000         $15,101,000
        Other comprehensive income:
          Foreign currency translation
            adjustment, net of tax                 (909,000)             91,000
          Unrealized gain on marketable
            securities, net of tax                  225,000             102,000
          Less: reclassification adjustment
            for gains realized in net
            income, net of tax                           --            (309,000)
                                                -----------         -----------
        Comprehensive income                    $17,777,000         $14,985,000
                                                ===========         ===========


Note 5

         The Company operates in one business segment, that is, as investment
advisors managing both domestic and international investment portfolios for
corporate, government and union benefit plans, mutual funds, individuals,
endowments, and foundations. Although each affiliated firm operates under its
own name with its own investment philosophy and approach, the firms' regulatory
environments and the economic characteristics of their products, services,
client bases and manner of distribution are similar. Therefore, the affiliated
firms are aggregated as one business segment.

         Revenues and long-lived assets shown below are classified according to
the affiliate's geographic location. The majority of the foreign long-lived
assets are domiciled in Canada. These Canadian assets totaled $137,157,000 and
$144,096,000 at March 31, 2000 and 1999, respectively. Revenues are derived
primarily from fees for investment advisory services provided to institutional
and other clients. These fees are generally a function of the overall fee rate
charged to each account and the level of assets under management by the
affiliated firms.

                                                Three Months Ended
                                                ------------------
                                    March 31, 2000               March 31, 1999
                                    --------------               --------------

Domestic revenues                    $ 218,978,000                $ 198,005,000
Foreign revenues                     $  20,070,000                $  19,690,000
Domestic long-lived assets           $ 837,101,000                $ 921,514,000
Foreign long-lived assets            $ 154,785,000                $ 161,398,000


                                      F-5
<PAGE>   9
Note 6

         Effective April 19, 2000, the Company entered into a closing agreement
with the Internal Revenue Service for the tax years 1984 through 1992. As part
of the agreement, all intangibles arising in taxable transactions prior to 1993
will be fully deductible over a 15-year life beginning with the date of
acquisition. The Company will make payments for certain previously deferred tax
accruals during the current year. As a result tax deductions will be increased
in current and future years.

ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
         AND RESULTS OF OPERATIONS

         The revenues of UAM's affiliated firms are derived primarily from fees
for investment advisory services provided to institutional and other clients.
Investment advisory fees are generally a function of the overall fee rate
charged to each account and the level of assets under management by the
affiliated firms. Assets under management can be affected by the addition of new
client accounts or client contributions to existing accounts, withdrawals of
assets from or terminations of client accounts, and investment performance,
which may depend on general market conditions.

         UAM's assets under management were $203.2 billion as of March 31, 2000,
compared to $202.6 billion at the start of the year. Investment performance
added $8.1 billion to assets under management during the quarter. This was
partially offset by negative net client cash flow of $7.0 billion. The sale of
an affiliate reduced assets under management by approximately $500 million.

                   AMORTIZATION OF COST ASSIGNED TO CONTRACTS

         Cost assigned to contracts acquired, net of accumulated amortization,
represented approximately 61% of the Company's total assets as of March 31,
2000. Amortization of cost assigned to contracts acquired, which is a non-cash
charge, represented 14% of the Company's operating expenses for the three months
ended March 31, 2000. Recording the cost assigned to contracts acquired as an
asset, with the resulting amortization as an operating expense, reflects the
application of generally accepted accounting principles to acquisitions by UAM
of investment management firms in transactions accounted for as purchases. The
principal assets acquired are the investment advisory contracts that evidence
the firms' ongoing relationships with their clients.

         The cost assigned to contracts acquired is amortized on a straight-line
basis over the estimated weighted average useful life of the contracts of
individual firms acquired. These lives are estimated through statistical
analysis of historical patterns of terminations and the size and age of the
contracts acquired as of the acquisition date.

         The Company regularly performs reviews of the remaining estimated lives
as well as for potential impairment of the value of acquired contracts. If any
review were to indicate that any of the estimated lives should be shortened, the
remaining cost assigned to contracts acquired would be amortized over the
shorter life commencing in the year in which the new estimate is determined. If
any review were to indicate that the carrying value of the contracts is
impaired, the asset would be adjusted to its estimated fair value.


                                      F-6
<PAGE>   10

         Cost assigned to contracts acquired is amortized as an operating
expense. It does not, however, require the use of cash and, therefore,
management believes that it is important to distinguish this expense from other
operating expenses in order to evaluate the performance of the Company.
Amortization of cost assigned to contracts acquired per share, referred to
below, has been calculated by dividing total amortization by the same number of
shares used in the diluted earnings-per-share calculation.


                                OPERATING RESULTS

                        THREE MONTHS ENDED MARCH 31, 2000
                                   COMPARED TO
                        THREE MONTHS ENDED MARCH 31, 1999

         Revenues were $239,048,000 for the three months ended March 31, 2000
compared to $217,695,000 for the first quarter of 1999. Revenues increased due
to positive market performance which generated higher fee revenues, partially
offset by the effect of negative client cash flows and the divestiture of three
small affiliates.

         Compensation and related expenses together with other operating
expenses were $163,323,000 compared to $148,215,000 in 1999, primarily
reflecting higher compensation earned by employees of existing affiliated firms
in accordance with revenue sharing plans, partially offset by lower operating
expenses. Amortization of cost assigned to contracts acquired was $26,294,000
compared to $26,088,000 in 1999. The increase was the result of the recording of
additional purchase price commitments associated with prior-year acquisitions,
partially offset by certain cost assigned to contracts acquired being fully
amortized at the end of 1999.

         Net interest expense increased to $16,789,000 from $15,834,000,
primarily as the result of an increase in the average interest rate charged on
borrowings, offset in part by lower average borrowings.

         Income before income tax expense was $31,503,000 compared to
$26,399,000 in 1999, reflecting the circumstances described above. The Company's
annual effective tax rate approximated 41% for the three-month period ended
March 31, 2000 compared to 43% in 1999.

         Net income was $18,461,000 compared to $15,101,000, reflecting the net
result of the events discussed above. Diluted earnings per share were $.33 for
the first quarter of 2000 compared to $.25 in the first quarter of 1999,
reflecting the effect of the Company's common stock repurchased and the
Company's lower average common stock price, partially offset by the impact of
the issuance of shares of common stock and the hypothetical exercise of warrants
and stock options on the calculation of earnings per share under the treasury
stock method. Amortization of cost assigned to contracts acquired per share
increased to $.46 in the first quarter of 2000 from $.43 in 1999 due to the
smaller number of shares outstanding. Net income plus amortization and
depreciation was $50,311,000 in the first quarter of 2000 compared to
$46,775,000 in 1999, and EBITDA (earnings before interest, taxes, depreciation
and amortization) was $80,142,000 in the first quarter of 2000 compared to
$73,907,000 in 1999 due to the circumstances discussed above. Management uses
the last two statistics not to the exclusion of net income, but rather as an
additional important measure of the Company's performance.


                                      F-7
<PAGE>   11

         CHANGES IN FINANCIAL CONDITION; LIQUIDITY AND CAPITAL RESOURCES

         The Company's internally generated cash totaled $50,311,000 for the
three months ended March 31, 2000. This cash and additional borrowings under the
Company's line of credit were primarily used to repurchase shares of the
Company's common stock and to pay dividends to shareholders. The Company invests
its excess cash in deposits with major banks, money market funds or in
securities, principally commercial paper, of companies with strong credit
ratings in diversified industries. As of March 31, 2000, the Company had drawn
down $333,000,000, leaving $417,000,000 available under its $750,000,000
Reducing Revolving Credit Agreement.

         Management believes that the Company's existing capital, together with
internally generated cash and borrowings available under its revolving line of
credit, will provide the Company with sufficient resources to meet its present
and reasonably foreseeable future cash needs. Management expects that the
principal uses of financial resources will be to provide further support for
investing in the growth initiatives of existing affiliates, satisfy deferred tax
obligations in connection with the IRS settlement, repurchase shares of the
Company's common stock, pay shareholder dividends, acquire additional investment
management firms, and to fund commitments due or potentially due to former
owners of affiliated firms.

         Increases or decreases in interest rates affect UAM's costs of
operations chiefly through raising or lowering the interest expense related to
the Company's variable-rate debt outstanding. To mitigate the risks associated
with increases in interest rates, UAM has entered into and plans to continue to
enter into interest-rate protection agreements. Rates of interest on the Senior
Notes and existing subordinated debt are fixed. Increases and decreases in
interest rates may also affect market prices of assets managed by the Company's
affiliated firms. Changes in such prices may affect the affiliated firms'
revenues, and therefore UAM's consolidated revenues.

                           FORWARD-LOOKING STATEMENTS

         This Quarterly Report on Form 10-Q contains "forward-looking"
statements. These statements include descriptions of UAM's operational plans,
expectations about future earnings and other results of operations, views of
future industry or market conditions, and other statements that include words
like "may," "expects," "believes," and "intends," and that describe opinions
about future events.

         Investors should not rely on these statements as though they were
guarantees. These statements are current only when they are made. UAM's
management has no obligation to revise or update these statements based on
future developments. Known and unknown risks may cause UAM's actual results and
performances to be materially different from those expressed or implied by these
statements. Some of these risks, uncertainties and other factors are that: most
of UAM's revenues are based on the market value of managed assets and,
therefore, will rise and fall with changes in the economy and financial markets;
the investment management business is highly competitive; the investment
management business is susceptible to internal shifts and frequently requires
firms to adapt; and UAM's affiliated firms depend significantly on key
employees. These and other factors are identified and more thoroughly explained
in Exhibit 99.1 to UAM's Annual Report on Form 10-K filed on March 21, 2000 with
the SEC.


                                      F-8
<PAGE>   12

ITEM 3.         QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

         The information provided below updates that which was previously
presented in Item 7A, Quantitative and Qualitative Disclosures About Market
Risk, of the Company's Form 10-K for the year ended December 31, 1999.

         The Company had $333,000,000 outstanding under its $750,000,000
Reducing Revolving Credit Agreement (the Credit Agreement) as of March 31, 2000.
Interest rates available for amounts outstanding under the Credit Agreement are
currently: prime, 1.875% over 30-day LIBOR or a money market bid option. In
addition, an annual commitment fee, payable on the daily average unused portion
of the Credit Agreement, is currently .375%. The effective interest rate on the
outstanding borrowings at March 31, 2000 was 7.9% compared to 6.5% at March 31,
1999. To mitigate against the risks associated with increases in interest rates,
the Company has entered into and plans to continue to enter into interest-rate
protection agreements with members of the Company's banking group. As of March
31, 2000, these agreements extend up to 18 months and limit interest rates to
no more than 10%.

         At March 31, 2000, the Company also had $179,886,000 of subordinated
notes outstanding which mature at various dates through March 2005 and have
interest rates ranging from 5.5% to 7.5%.


                                      F-9