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

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

                                    FORM 10-K

                        FOR ANNUAL AND TRANSITION REPORTS
                    PURSUANT TO SECTIONS 13 OR 15 (d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

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

                   FOR THE FISCAL YEAR ENDED DECEMBER 31, 1998
                                       OR
             [ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15 (d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934


                         COMMISSION FILE NUMBER 0-16358


                              ANDOVER BANCORP, INC.
             (Exact name of registrant as specified in its charter)


               DELAWARE                                           04-2952665
    (State or other jurisdiction of                           (I.R.S. Employer
     incorporation or organization)                          Identification No.)


      61 MAIN STREET, ANDOVER, MA                                  01810
(Address of principal executive office)                          (Zip Code)

        REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE: (978)749-2000

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

           SECURITIES REGISTERED PURSUANT TO SECTION 12(b) OF THE ACT:

                                      NONE

           SECURITIES REGISTERED PURSUANT TO SECTION 12(g) OF THE ACT:

                          COMMON STOCK, $0.10 PAR VALUE
                                (Title of Class)
                        PREFERRED STOCK PURCHASED RIGHTS
                                (Title of Class)

     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 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. 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 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. [ ]

     The aggregate market value of the voting stock held by non-affiliates of
the Registrant, based on the closing sale price for the Registrant's Common
Stock on March 1, 1999, as reported by NASDAQ, was $198,142,564.50.

     The number of shares outstanding of each of the Registrant's classes of
Common Stock, as of the latest practicable date, is:

                 Class: Common Stock, par value $0.10 per share
                Outstanding as of March 1, 1999: 6,523,212 shares

                       DOCUMENTS INCORPORATED BY REFERENCE

     Portions of the Andover Bancorp, Inc. Definitive Notice of Annual Meeting
and Proxy Statement for the 1999 Annual Meeting of Shareholders are incorporated
by reference into Part III of Form 10-K.

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                                    FORM 10-K
                              CROSS REFERENCE INDEX

                                                                         Annual
                                                                         Report
                                                                          Page


                                     PART I

Item 1    Business...........................................................2

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 Registrant's Common Equity and Related Stockholder 
          Matters............................................................9

Item 6    Selected Consolidated Financial Data..............................10

Item 7    Management's Discussion and Analysis of Financial Condition and
          Results of Operations.............................................11

Item 7A   Quantitative and Qualitative Disclosures About Market Risk........27

Item 8    Financial Statements and Supplementary Data................(See Item
                                                                     14 below)

Item 9    Changes in and Disagreements with Accountants on Accounting 
          and Financial Disclosure........................................Non-
                                                                    Applicable

                                    PART III

The information called for by Part III (Items 10 through 13) is incorporated
herein by reference from Andover's Definitive Notice of Annual Meeting and Proxy
Statement for the 1999 Annual Meeting of Stockholders to be filed with the
Securities and Exchange Commission.

                                     PART IV

Item 14   Exhibits, Financial Statement Schedules and Reports on Form 8-K

(a)(1)    Financial Statements-
           Independent Auditors' Report.....................................35

           Consolidated Balance Sheets as of December 31, 1998 and 1997.....36

           Consolidated Statements of Operations for each of the years 
           ended December 31, 1998, 1997 and 1996...........................37

           Consolidated Statements of Changes in Stockholders' Equity
           for each of the years ended December 31, 1998, 1997 and 1996.....38

           Consolidated Statements of Cash Flows for each of the years 
           ended December 31, 1998, 1997 and 1996........................39-40

           Notes to Consolidated Financial Statements....................41-64





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(2)           All financial statement schedules are omitted because they are not
              applicable, the data is not significant, or the required
              information is shown elsewhere in this report.

(b)           Reports on Form 8-K. There were no reports filed on Form 8-K
              during the three months ended December 31, 1998.

(c)           List of Exhibits

              Exhibits to the Form 10-K have been included only with the copies
              of the Form 10-K filed with the SEC. Upon request to Shareholder
              Relations, Andover Bancorp, Inc., 61 Main Street, Andover,
              Massachusetts 01810, copies of the individual exhibits will be
              furnished upon payment of a reasonable fee.


EXHIBIT NO.   DESCRIPTION OF EXHIBITS
-----------   -----------------------

3.1           Restated Certificate of Incorporation of Andover (incorporated
              herein by reference to Exhibit 3.1 to Post-Effective Amendment No.
              1 to Andover's Registration Statement on Form S-4, No. 33-11891
              filed on March 5, 1987).

3.2           By-laws of Andover, as amended and restated, January 23, 1997
              (incorporated herein by reference to Exhibit 3.2 to Andover's Form
              10-K for the fiscal year ended December 31, 1996).

4.1           Specimen of Andover Bancorp, Inc. common stock certificate
              (incorporated herein by reference to Exhibit 4 to Andover's
              Registration Statement on Form S-4, Registration No. 33-11891,
              filed on February 11, 1987).

4.2           Shareholder Rights Agreement between Andover Bancorp, Inc. and
              BankBoston (incorporated herein by reference to an Exhibit to
              Andover's Current Report on Form 8-K filed on January 22, 1999).

10.1          Employment Agreement between Andover, Andover Bank and Gerald T.
              Mulligan, dated May 16, 1991 (incorporated herein by reference to
              Exhibit 10.1 to Andover's Form 10-K for the fiscal year ended
              December 31, 1991).

10.2          Special Termination Agreement between Andover, Andover Bank and
              Gerald T. Mulligan, dated May 16, 1991, as amended and restated
              through January 23, 1997 (incorporated herein by reference to
              Exhibit 10.2 to Andover's Form 10-K for the fiscal year ended
              December 31, 1996).

10.3          Special Termination Agreement between Andover, Andover Bank and
              Joseph F. Casey, dated December 17, 1992, as amended and restated
              through January 23, 1997 (incorporated herein by reference to
              Exhibit 10.3 to Andover's Form 10-K for the fiscal year ended
              December 31, 1996).

10.4          Special Termination Agreement between Andover, Andover Bank and
              Michael J. Ecker, dated December 17, 1992, as amended and restated
              through January 23, 1997 (incorporated herein by reference to
              Exhibit 10.4 to Andover's Form 10-K for the fiscal year ended
              December 31, 1996).

10.5          Special Termination Agreement between Andover, Andover Bank and
              John R. Heerwagen, dated December 17, 1992, as amended and
              restated through January 23, 1997 (incorporated herein by
              reference to Exhibit 10.5 to Andover's Form 10-K for the fiscal
              year ended December 31, 1996).

10.6          Special Termination Agreement between Andover, Andover Bank and
              Octavio C. Bolivar dated January 24, 1994, as amended and
              restated, January 23, 1997 (incorporated herein by reference to
              Exhibit 10.6 to Andover's Form 10-K for the fiscal year ended
              December 31, 1996).





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<PAGE>   4
10.7          Andover Savings Bank Employees' Stock Ownership Plan and Trust
              Agreement and Amendment No. 1 (incorporated herein by reference to
              Exhibit 10(c) to Andover's Annual Report on Form 10-K for the
              fiscal year ended December 31, 1987).

10.8          Andover Bancorp, Inc. Stock Option Plan dated May 8, 1986, as
              amended May 22, 1986, January 29, 1987, and November 2, 1987
              (incorporated herein by reference to Exhibit 10(h) to Andover's
              Annual Report on Form 10-K for the fiscal year ended December 31,
              1987).

10.9          Special Termination Agreement between Andover, Andover Bank and
              Raymond P. Smith, dated December 12, 1995, as amended and
              restated, January 23, 1997 (incorporated herein by reference to
              Exhibit 10.9 to Andover's Form 10-K for the fiscal year ended
              December 31, 1996).

10.10         Andover Bancorp, Inc. 1995 Stock Incentive Plan, dated February
              16, 1995 (incorporated herein by reference to Exhibit 10.11 to
              Andover's Annual Report on Form 10-K for the fiscal year ended
              December 31, 1995).

10.11         Deferred Compensation Plan for Directors of Andover Bancorp, Inc.
              and its Subsidiaries, effective July 1, 1993, as amended and
              restated, February 22, 1996 (incorporated herein by reference to
              Exhibit 10.12 to Andover's Annual Report on Form 10-K for the
              fiscal year ended December 31, 1995).

10.12         Andover Bancorp, Inc. Special Termination Plan, effective January
              23, 1997 (incorporated herein by reference to Exhibit 10.12 to
              Andover's Form 10-K for the fiscal year ended December 31, 1996).

11            The computation of per share earnings can be readily determined
              from the material contained in the Annual Report on Form 10-K for
              the fiscal year ended December 31, 1998.

12            As the Company does not have any debt securities registered under
              Section 12 of the Securities Act of 1933, no ratio of earnings to
              fixed charges appears in this Annual Report on Form 10-K.

13            Andover Bancorp, Inc. 1998 Annual Report, which, except for those
              portions expressly incorporated herein by reference, is furnished
              only for the information of the Securities and Exchange Commission
              and is not deemed to be filed.

21            The Company has two subsidiaries, Andover Bank and Andover Bank
              NH. Andover Bank is a Massachusetts savings bank in stock form
              while Andover Bank NH is a New Hampshire guaranty savings bank in
              stock form. Both subsidiaries are included in the Consolidated
              Financial Statements filed in the Annual Report on Form 10-K for
              the fiscal year ended December 31, 1998.

23.1          Consent of KPMG Peat Marwick LLP.

27            Financial Data Schedule



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                                   SIGNATURES

     Pursuant to the requirements of Section 13 of the Securities Exchange Act
of 1934, the Company has duly caused this report to be signed on its behalf by
the undersigned, thereunto duly authorized.

                                              ANDOVER BANCORP, INC.




March 17, 1999                                By: /s/ Gerald T. Mulligan
                                                  -----------------------------
                                                  Gerald T. Mulligan, President
                                                  and Chief Executive Officer



     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 Company
and in the capacities and on the dates indicated.

Signature                        Title                           Date

/s/ Gerald T. Mulligan           President, Chief                March 17, 1999
-------------------------        Executive Officer and
Gerald T. Mulligan               Director (Principal
                                 Executive Officer)

/s/ Joseph F. Casey              Chief Financial Officer         March 17, 1999
-------------------------        and Treasurer (Principal
Joseph F. Casey                  Financial and Accounting
                                 Officer)


/s/ Thomas F. Caffrey            Director                        March 17, 1999
-------------------------
Thomas F. Caffrey

/s/ Naomi A. Gardner             Director                        March 17, 1999
-------------------------
Naomi A. Gardner

/s/ Cornelius J. Mccarthy        Director                        March 17, 1999
-------------------------
Cornelius J. McCarthy

/s/ Clifford E. Elias            Director                        March 17, 1999
-------------------------
Clifford E. Elias

/s/ Robert J. Scribner           Director                        March 17, 1999
-------------------------
Robert J. Scribner

/s/ Fred P. Shaheen              Director                        March 17, 1999
-------------------------
Fred P. Shaheen






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<PAGE>   6
                              EXHIBITS TO FORM 10-K
                              ANDOVER BANCORP, INC.

                                  EXHIBIT INDEX

EXHIBIT NO. DESCRIPTION OF EXHIBIT                                      PAGE NO.
----------- ----------------------                                      --------

3.1         Restated Certificate of Incorporation of Andover
            (incorporated herein by reference to Exhibit 3.1 to
            Post-Effective Amendment No. 1 to Andover's Registration
            Statement on Form S-4, No. 33-11891 filed on March 5,
            1987).                                                         --

3.2         By-laws of Andover, as amended and restated, January 23,
            1997 (incorporated herein by reference to Exhibit 3.2 to
            Andover's Form 10-K for the fiscal year ended December 31,
            1996).                                                         --

4.1         Specimen of Andover Bancorp, Inc. common stock certificate
            (incorporated herein by reference to Exhibit 4 to
            Andover's Registration Statement on Form S-4, Registration
            No. 33-11891, filed on February 11, 1987).                     --

4.2         Shareholder Rights Agreement between Andover Bancorp, Inc.
            and BankBoston (incorporated herein by reference to an
            Exhibit to Andover's Current Report on Form 8-K (filed
            January 22, 1999).                                             --

10.1        Employment Agreement between Andover, Andover Bank and
            Gerald T. Mulligan, dated May 16, 1991 (incorporated
            herein by reference to Exhibit 10.1 to Andover's Form 10-K
            for the fiscal year ended December 31, 1991).                  --

10.2        Special Termination Agreement between Andover, Andover
            Bank and Gerald T. Mulligan, dated May 16, 1991, as
            amended and restated through January 23, 1997
            (incorporated herein by reference to Exhibit 10.2 to
            Andover's Form 10-K for the fiscal year ended December 31,
            1996).                                                         --





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<PAGE>   7
10.3        Special Termination Agreement between Andover, Andover
            Bank and Joseph F. Casey, dated December 17, 1992, as
            amended and restated through January 23, 1997
            (incorporated herein by reference to Exhibit 10.3 to
            Andover's Form 10-K for the fiscal year ended December 31,
            1996).                                                         --

10.4        Special Termination Agreement between Andover, Andover
            Bank and Michael J. Ecker, dated December 17, 1992, as
            amended and restated through January 23, 1997
            (incorporated herein by reference to Exhibit 10.4 to
            Andover's Form 10-K for the fiscal year ended December 31,
            1996).                                                         --

10.5        Special Termination Agreement between Andover, Andover
            Bank and John R. Heerwagen, dated December 17, 1992, as
            amended and restated through January 23, 1997
            (incorporated herein by reference to Exhibit 10.5 to
            Andover's Form 10-K for the fiscal year ended December 31,
            1996).                                                         --

10.6        Special Termination Agreement between Andover, Andover
            Bank and Octavio C. Bolivar, dated January 24, 1994 as
            amended and restated, January 23, 1997 (incorporated
            herein by reference to Exhibit 10.6 to Andover's Form 10-K
            for the fiscal year ended December 31, 1996).                  --

10.7        Andover Savings Bank Employees' Stock Ownership Plan and
            Trust Agreement and Amendment No. 1 (incorporated herein
            by reference to Exhibit 10(c) to Andover's Annual Report
            on Form 10-K for the fiscal year ended December 31, 1987).     --

10.8        Andover Bancorp, Inc. Stock Option Plan dated May 8, 1986,
            as amended May 22, 1986, January 29, 1987 and November 2,
            1987 (incorporated herein by reference to Exhibit 10(h) to
            Andover's Annual Report on Form 10-K for the fiscal year
            ended December 31, 1987).                                      --

10.9        Special Termination Agreement between Andover, Andover
            Bank and Raymond P. Smith, dated December 12, 1995, as
            amended and restated, January 23, 1997 (incorporated
            herein by reference to Exhibit 10.9 to Andover's Form 10-K
            for the fiscal year ended December 31, 1996).                  --





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<PAGE>   8
10.10       Andover Bancorp, Inc. 1995 Stock Incentive Plan, dated
            February 16, 1995 (incorporated herein by reference to
            Exhibit 10.11 to Andover's Annual Report on Form 10-K for
            the fiscal year ended December 31, 1995).                      --

10.11       Deferred Compensation Plan for Directors of Andover
            Bancorp, Inc. and its Subsidiaries, effective July 1,
            1993, as amended and restated, February 22, 1996
            (incorporated herein by reference to Exhibit 10.12 to
            Andover's Annual Report on Form 10-K for the fiscal year
            ended December 31, 1995).                                      --

10.12       Andover Bancorp, Inc. Special Termination Plan, effective
            January 23, 1997 (incorporated herein by reference to
            Exhibit 10.12 to Andover's Form 10-K for the fiscal year
            ended December 31, 1996).                                      --

11          The computation of per share earnings can be readily
            determined from the material contained in the Annual
            Report on Form 10-K for the fiscal year ended December 31,
            1998.                                                          --

12          As the Company does not have any debt securities
            registered under Section 12 of the Securities Act of 1933,
            no ratio of earnings to fixed charges appears in this
            Annual Report on Form 10-K.                                    --

13          Andover Bancorp, Inc. 1998 Annual Report, which, except
            for those portions expressly incorporated herein by
            reference, is furnished only for the information of the
            Securities and Exchange Commission and is not deemed to be
            filed.                                                          9

21          The Company has two subsidiaries, Andover Bank and Andover
            Bank NH. Andover Bank is a Massachusetts savings bank in
            stock form while Andover Bank NH is a New Hampshire
            guaranty savings bank in stock form. Both subsidiaries are
            included in the Consolidated Financial Statements filed in
            the Annual Report on Form 10-K for the fiscal year ended
            December 31, 1998.                                             --

23.1        Consent of KPMG Peat Marwick LLP.                              85




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