Exhibit 5.1

April 28, 2020

Randolph Bancorp, Inc.

10 Cabot Place

Stoughton, MA 02072

Re: Securities Being Registered under Registration Statement on Form S-8

Ladies and Gentlemen:

We have acted as counsel to you in connection with your filing of a Registration Statement on Form S-8 (the “Registration Statement”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), on or about the date hereof relating to an aggregate of 59,118 shares (the “Shares”) of Common Stock, $0.01 par value per share, of Randolph Bancorp, Inc., a Massachusetts corporation (the “Company”), that may be issued pursuant to the Company’s Inducement Non-Qualified Stock Option Agreement and Inducement Restricted Stock Award Agreement between the Company and William M. Parent and Inducement Non-Qualified Stock Option Agreement and Inducement Restricted Stock Award Agreement between the Company and Lauren B. Messmore (collectively, the “Inducement Agreements”).

We have reviewed such documents and made such examination of law as we have deemed appropriate to give the opinions set forth below. We have relied, without independent verification, on certificates of public officials and, as to matters of fact material to the opinion set forth below, on certificates of the Company.

The opinion set forth below is limited to the Massachusetts Business Corporations Act.

For purposes of the opinion set forth below, we have assumed that a sufficient number of authorized but unissued shares of the Company’s Common Stock will be available for issuance when the Shares are issued.

Based on the foregoing, we are of the opinion that the Shares have been duly authorized and, upon issuance and delivery against payment therefor in accordance with the terms of the Inducement Agreements, will be validly issued, fully paid and nonassessable.

We hereby consent to the inclusion of this opinion as Exhibit 5.1 to the Registration Statement. In giving our consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations thereunder.

Very truly yours,

/S/ Goodwin Procter LLP

GOODWIN PROCTER LLP