The Boston Redevelopment Authority has approved construction of 38-story residential tower behind the TD Garden that will include more than 500 apartments, restaurants, and stores.

AvalonBay Communities Inc. will build the tower on Nashua Street, filling empty space between the Garden and the Charles River. The $200 million project, approved by the BRA board Thursday night, also includes construction of a two-story retail arcade that will connect the new tower to Causeway Street and North Station.