Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the Registration Statement of Meridian Bancorp, Inc. on Form S-8 (SEC File No. 333-198686) of our report dated June 26, 2019 appearing in this Annual Report on Form 11-K of the East Boston Savings Bank 401(k) Plan for the year ended December 31, 2018.

/s/ Wolf & Company, P.C.

Boston, Massachusetts

June 26, 2019