
<PAGE>
 
                                                                     Exhibit 5.1


                           GOODWIN PROCTER & HOAR LLP

                               COUNSELLORS AT LAW
                                 EXCHANGE PLACE
                        BOSTON, MASSACHUSETTS 02109-2881



                                 July 30, 1998



Boston Properties, Inc.
8 Arlington Street
Boston, MA  02116

Ladies and Gentlemen:

     This opinion is furnished in connection with the registration on Form S-3
(the "Registration Statement") pursuant to the Securities Act of 1933, as
amended (the "Securities Act"), of 2,678,774 shares of common stock (the
"Redemption Shares"), par value $.01 per share ("Common Stock"), of Boston
Properties, Inc., a Delaware corporation (the "Company"), if and to the extent
that holders of units of limited partnership ("Units") in Boston Properties
Limited Partnership (the "Operating Partnership") tender such Units to the
Operating Partnership for redemption and the Company exercises its contractual
right to acquire such tendered Units for Redemption Shares.

     In connection with rendering this opinion, we have examined the Amended and
Restated Certificate of Incorporation and Amended and Restated Bylaws of the
Company, each as amended to date; such records of the corporate proceedings of
the Company as we deemed material; 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.
<PAGE>
 
Boston Properties, Inc.
July 30, 1998
Page 2

     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 laws of The Commonwealth of
Massachusetts, and the Delaware General Corporation Law.

     Based upon the foregoing, we are of the opinion that when Redemption Shares
have been issued in exchange for Units tendered to the Operating Partnership for
redemption as contemplated by the limited partnership agreement of the Operating
Partnership, such Redemption Shares will be validly issued, fully paid and
nonassessable.

     The foregoing assumes that all requisite steps were 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 the filing of this opinion as an exhibit to the
Registration Statement and to the reference to us with respect to this opinion
under the heading "Legal Matters" in the Prospectus which is a part of such
Registration Statement.  In giving such consent, we do not thereby admit that we
are in the category of persons whose consent is required under Section 7 of the
Act.

                                    Very truly yours,

                                    /s/ Goodwin, Procter & Hoar LLP

                                    GOODWIN, PROCTER & HOAR LLP
