Exhibit 99.1

10 Cabot Place, Stoughton, MA 02072

RANDOLPH BANCORP, INC. COMPLETES STOCK OFFERING AND ACQUISITION OF FIRST EASTERN BANKSHARES CORPORATION

STOUGHTON, Massachusetts – Randolph Bancorp, Inc. (the “Company”), a Massachusetts corporation and the holding company for Randolph Savings Bank (the “Bank”), announced today the completion of the Company’s mutual-to-stock conversion and stock offering. Shares of Randolph Bancorp, Inc. common stock will begin trading on July 1, 2016, on the NASDAQ Global Market under the symbol “RNDB.”

The Company also announced that it had completed the acquisition of First Eastern Bankshares Corporation (“First Eastern”) and its wholly-owned subsidiary, First Federal Savings Bank of Boston. First Federal’s primary business is the origination and sale of residential mortgage loans in the secondary market and offering a variety of insured deposit accounts and using such deposits as well as borrowings to originate loans, primarily residential mortgage loans, to its customers. The Company expects that the acquisition of First Eastern will allow it to significantly grow its mortgage business while also adding depth to its team of mortgage professionals. The acquisition will also expand the Company’s footprint to include a branch office in downtown Boston, seven loan production offices in Massachusetts and one loan production office in New Hampshire.

The Company sold 5,686,750 shares of common stock, representing the adjusted maximum of the offering range, at $10.00 per share, for gross offering proceeds of $56,867,500, including the sale of 469,498 shares to the employee stock ownership plan in the stock offering. Additionally, 181,976 shares of Company common stock and $454,940 in cash have been contributed to The Randolph Savings Charitable Foundation, Inc. in connection with the conversion and offering.

As previously announced, the stock offering was oversubscribed in the first category of the subscription offering by eligible depositors as of December 31, 2014. Accordingly, eligible depositors will have valid orders filled in accordance with the allocation procedures described in the prospectus and as set forth in the Plan of Conversion.

“We appreciate the support that we have received from our depositors during this process and welcome our new shareholders,” stated James P. McDonough, the Company’s President and Chief Executive Officer. “We are also looking forward to welcoming customers of First Federal Savings Bank. We know they will benefit from our expanded product offerings as well as our technology based services which allow our customers to bank anywhere and anytime they want.”

If you are a first category subscriber and would like to confirm your allocation, you may contact the Stock Information Center at (877) 821-5783 (toll free) from 10:00 a.m. until 4:00 p.m., Eastern Time, Monday through Friday. This information is also available online at https://allocations.kbw.com/.

Keefe, Bruyette & Woods, Inc., A Stifel Company acted as selling agent in the subscription offering, and served as financial advisor to the Company and the Bank in connection with the conversion. Goodwin Procter LLP, Boston, MA, served as legal counsel to the Company and the Bank in connection with the conversion and the acquisition. Luse Gorman, PC, Washington, DC, served as legal counsel to the selling agent in connection with the conversion. Murphy & King, P.C., Boston, MA, served as counsel to First Eastern in connection with the acquisition.

Forward-Looking Statements

This press release contains certain forward-looking statements about the conversion, the stock offering and the acquisition. Forward-looking statements include statements regarding anticipated future events and can be identified by the fact that they do not relate strictly to historical or current facts. They often include words such as “believe,” “expect,” “anticipate,” “estimate,” and “intend” or future or conditional verbs such as “will,” “would,” “should,” “could,” or “may.” Forward-looking statements, by their nature, are subject to risks and uncertainties. Certain factors that could cause actual results to differ materially from expected results include increased competitive pressures, changes in the interest rate environment, general economic conditions or conditions within the securities markets, and legislative and regulatory changes that could adversely affect the business in which the Company and Bank are engaged.