Nathanael Greene's keel was laid down on 21 May 1962 at the Portsmouth Naval Shipyard in Kittery, Maine. She was launched on 12 May 1964, sponsored by Mrs. Neander W. Wade, a descendant of Nathanael Greene, and commissioned on 19 December 1964 with Commander Robert E. Crispin in command of the Blue Crew and Commander William M. Cossaboom in command of the Gold Crew.