Watson was commissioned lieutenant on 4 October 1780, and in May 1783 recommissioned the cutter Mutine 14, commanding her until she was paid off in 1787. He was promoted commander on 1 December 1787.
In May 1790 he recommissioned the fireship Spitfire 8, which was attached to the Grand Fleet during the Spanish Armament, and he was posted captain with seniority from 25 October 1790.
Watson’s only post command was the Isis 50, which he joined in the summer of 1795 and which was with the squadron that captured the Dutch frigate Alliantie 36 on 22 August. In 1796 she was sent to St. Helena to bring home the trade.
Four days after the outbreak of the mutiny in the North Sea squadron on 27 May 1797 the crew of the Isis rose against their officers and sailed to join the mutiny at the Nore. By the time she fought at the Battle of Camperdown on 11 October Watson was no longer in command, having been succeeded in the previous month by Captain William Mitchell.
He became a rear-admiral on 28 April 1808, a vice-admiral on 4 December 1813, and having retired to Yealmpton in Devon he died on 20 March 1819.
Both Watson’s widow and a daughter died in Yealmpton during 1830.