Exhibit 5.1

Suite 900 607 14th St., NW

Washington DC 20005-2018

t 202 508 5800 f 202 508 5858

Board of Directors

Wellesley Bancorp, Inc.

40 Central Street

Wellesley, Massachusetts 02482

Ladies and Gentlemen:

We have acted as special counsel for Wellesley Bancorp, Inc., a Maryland corporation (the “Company”), in connection with the Registration Statement on Form S-1 (the “Registration Statement”) initially filed by the Company on September 9, 2011 with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Act”), and the regulations promulgated thereunder.

Pursuant to a Plan of Conversion adopted by the Board of Directors of Wellesley Bank (the “Bank”), the Registration Statement relates to: (i) the proposed issuance and sale by the Company of up to 3,174,000 shares (the “Offering Shares”) of common stock, $0.01 par value per share, of the Company (the “Common Stock”) in a subscription offering, a community offering and a syndicated community offering (the “Offerings”) and (ii) the proposed issuance and contribution of 222,180 shares of Common Stock (the “Foundation Shares”) to the Wellesley Bank Charitable Foundation, a charitable foundation (the “Foundation”).

In the preparation of this opinion, we have examined originals or copies identified to our satisfaction of: (i) the Company’s articles of incorporation; (ii) the Company’s bylaws; (iii) the Registration Statement, including the prospectus contained therein and the exhibits thereto; (iv) certain resolutions of the Board of Directors of the Company relating to the issuance of the Common Stock being registered under the Registration Statement; (v) the Plan of Conversion; (vi) the trust agreement for the Bank’s employee stock ownership plan (the “ESOP”) and the form of loan agreement between the Company and the ESOP; and (vii) the form of stock certificate approved by the Board of Directors of the Company to represent shares of the Common Stock. We have also examined originals or copies of such documents, corporate records, certificates of public officials and other instruments, and have conducted such other investigations of law and fact, as we have deemed necessary or advisable for purposes of our opinion.

ATLANTA   AUGUSTA   CHARLOTTE   DENVER  DUBAI   NEW YORK   OAKLAND   PALO   ALTO   RALEIGH   SAN DIEGO   SAN FRANCISCO   SEATTLE   STOCKHOLM   TAIPEI   TOKYO   WALNUT   CREEK   WASHINGTON, DC   WINSTON-SALEM

Board of Directors

Wellesley Bancorp, Inc.

October 25, 2011

Page 2

In our examination, we have relied on the genuineness of all signatures, the authenticity of all documents and instruments submitted to us as originals, and the conformity to the originals of all documents and instruments submitted to us as certified or conformed copies. In addition, we have relied on the accuracy and completeness of all records, documents, instruments and materials made available to us by the Company.

Our opinion is limited to the matters set forth herein, and we express no opinion other than as expressly set forth herein. In rendering the opinions set forth below, we do not express any opinion concerning law other than the laws of the State of Maryland.

For purposes of this opinion, we have assumed that, prior to the issuance of any shares of Common Stock, (i) the Registration Statement, as finally amended, will have become effective under the Act and (ii) the conversion of the Bank will have become effective.

Based upon and subject to the foregoing, it is our opinion that, upon the due adoption by the Board of Directors of the Company (or authorized committee thereof) of a resolution fixing the number of Offering Shares to be sold in the Offerings and the number of Foundation Shares to be contributed to the Foundation, such Offering Shares, when issued and sold in the manner described in the Registration Statement, and such Foundation Shares, when issued and contributed to the Foundation in the manner described in the Registration Statement, will, in each case, be validly issued, fully paid and nonassessable.

We consent to the filing of this opinion as an exhibit to the Registration Statement and to the reference to our firm under the heading “Legal and Tax Opinions” in the prospectus which is part of the Registration Statement, as such may be amended or supplemented, or incorporated by reference in any Registration Statement covering additional shares of Common Stock to be issued or sold under the Plan of Conversion that is filed pursuant to Rule 462(b) under the Act. In giving such consent, we do not hereby admit that we are experts or are otherwise within the category of persons whose consent is required under Section 7 of the Act or the rules or regulations of the Securities and Exchange Commission thereunder.