
<PAGE>

                                                                     Exhibit 5.1

                           GOODWIN, PROCTER & HOAR LLP

                               COUNSELLORS AT LAW
                                 EXCHANGE PLACE
                        BOSTON, MASSACHUSETTS 02109-2881


                                  June 22, 1999

Boston Properties, Inc.
800 Boylston Street
Boston, Massachusetts 02199

     Re:  Legality of Securities to be Registered Under
          Registration Statement on Form S-3
          ---------------------------------------------

Ladies and Gentlemen:

     This opinion is furnished in connection with the registration statement on
Form S-3 (the "Registration Statement") pursuant to the Securities Act of 1933,
as amended (the "Securities Act"), relating to the registration of 1,500,000
shares of common stock, par value $.01 per share (the "Common Stock"), of Boston
Properties Inc., a Delaware corporation (the "Company"), that may be issued by
the Company pursuant to the Company's Dividend Reinvestment and Stock Purchase
Plan (the "Plan").

     In connection with rendering this opinion, we have examined the Amended and
Restated Certificate of Incorporation of the Company, as amended and restated to
the date hereof and on file with the Office of the Secretary of State of
Delaware; the Bylaws of the Company, as amended to the date hereof; such records
of the corporate proceedings of the Company as we deemed material; the
Registration Statement and the exhibits thereto; and such other certificates,
receipts, records and documents as we considered necessary for the purposes of
this opinion. In our examination, we have assumed the genuineness of all
signatures, the legal capacity of natural persons, the authenticity of all
documents submitted to us as certified, photostatic or facsimile copies, the
authenticity of the originals of such copies and the authenticity of telephonic
confirmations of public officials and others. As to facts material to our
opinion, we have relied upon certificates or telephonic confirmations of public
officials and certificates, documents, statements and other information of the
Company or representatives or officers thereof.

     We are attorneys admitted to practice in The Commonwealth of Massachusetts.
We express no opinion concerning the laws of any jurisdictions other than the
laws of the United States of America, The Commonwealth of Massachusetts and the
Delaware General
<PAGE>

Boston Properties, Inc.
June 22, 1999
Page 2


Corporation Law and also express no opinion with respect to the blue sky or
securities laws of any state, including Massachusetts and Delaware.

     Based upon the foregoing, we are of the opinion that when the shares of
Common Stock registered under the Registration Statement have been issued and
the Company has received full payment for the Common Stock in accordance with
the terms of the Plan, such shares will be validly issued, fully paid and
non-assessable shares of Common Stock.

     The foregoing assumes that all requisite steps will be taken to comply with
the requirements of the Securities Act and applicable requirements of state laws
regulating the offer and sale of securities.

     We hereby consent to being named as counsel to the Company in the
Registration Statement, to the references therein to our firm under the caption
"Legal Matters" and to the inclusion of this opinion as an exhibit to the
Registration Statement.

                                    Very truly yours,

                                    /s/ Goodwin, Procter & Hoar LLP

                                    GOODWIN, PROCTER & HOAR  LLP
