Henry M. Jackson originally was to have been named Rhode Island. The contract to build Rhode Island was awarded to the Electric Boat Division of General Dynamics Corporation at Groton, Connecticut, on 6 June 1977 and her keel was laid down there on 19 January 1981. Shortly after Senator Jackson suddenly died in office on 1 September 1983, Rhode Island was renamed Henry M. Jackson, and the name Rhode Island was transferred to another Ohio-class submarine, USS Rhode Island (SSBN-740).
Henry M. Jackson was launched on 15 October 1983, sponsored by Senator Jackson's daughter, Ms. Anna Marie Jackson, and commissioned on 6 October 1984, with Captain R. Tindal in command of the Blue Crew and Captain M. A. Farmer in command of the Gold Crew.