The Federal Reserve Board said Thursday that it had approved Brookline Bancorp Inc.’s acquisition of Bancorp Rhode Island Inc. in Providence, R.I.

The $3.1 billion-asset Brookline, Mass., company said in April that it would pay $234 million in cash and stock for the $1.6 billion-asset Bancorp Rhode Island, which is based in Providence. Brookline had extended a shareholder election deadline several times, including last Friday when it was pushed back until Dec. 16, as it awaited the Fed’s blessing.

Brookline had previously said that it would keep Bancorp Rhode Island as a state charter and operate its BankRI as a separate unit.

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