"Agamemnon" was ordered from the commercial shipbuilder Henry Adams at his Bucklers Hard shipyard on the Beaulieu River on 5 February 1777, to be built to the lines of the , as designed by Sir Thomas Slade. Her keel was laid down in May. She was constructed using timber sourced from the surrounding New Forest. The total cost of her construction was £38,303 15s 4d. She was commissioned on 28 March 1781 under Captain Benjamin Caldwell—a full 13 days before her launch on 10 April.