He was commissioned lieutenant on 24 June 1762 and saw duty aboard the Pearl 32, Captain Charles Saxton, being her senior lieutenant when she was paid off in 1766 after service on the Newfoundland station.
During the winter of 1776-7 Watt was a junior lieutenant aboard the Eagle 64, Captain Henry Duncan, flagship to Vice-Admiral Lord
Howe in North American waters, and as the first lieutenant of the Roebuck 44, Captain Andrew Snape Hamond, he participated in the Philadelphia campaign from August – November 1777. Having been placed in command of the captured American frigate Delaware by Hamond with a scratch crew in the river of that name, he destroyed a number of rebel privateers. Upon Lord Howe confirming the appointment he was promoted commander with effect from 23 November.
On 2 July 1778 he joined the fireship Sulphur 8, commanding her in Vice-Admiral Lord Howe’s fleet in the defence of New York during July and being present at the action with d’Estaing off Rhode Island in August before returning to England in the following year.
Watt was posted captain on 9 May 1781 and recommissioned the Sultan 74, sailing for the East Indies in the summer and joining the fleet in March, by which time his command was ridden with scurvy. He fought at the Battle of Providien on 12 April 1782 where nine of his men were men wounded,and at the Battle of Negapatam on 6 July where he lost sixteen men killed and twenty-one wounded. During the action a French 64 lowered her colours to him but later re-hoisted them and rejoined her consorts. Watt was sent by Vice-Admiral Sir Edward Hughes Hughes under a flag of truce to claim the 64 as a prize, but this demand was rejected by Commodore Suffren.
Watt died as a result of injuries incurred at the Battle of Trincomale on 3 September 1782.