The Federal Reserve board on Tuesday approved a deal that will create the fourth biggest local bank: Century City’s PacWest Bancorp’s acquisition of downtown L.A. CapitalSource Inc.

That’s the last approval needed for the deal, which had already been OK’d by the Federal Deposit Insurance Corp. and the California Department of Business Oversight.

Under the acquisition, business lender CapitalSource Bank will become part of PacWest’s Pacific Western Bank. That will pump Pacific Western’s total assets to $15.4 billion and make it the fourth largest bank by assets in Los Angeles County, following City National Bank, East West Bank and OneWest Bank; and the 14th largest in the state.

Officials at the two banks have not announced when the deal will close, but had said last week that they expected to close soon after Federal Reserve approval.