Wallis was born near Camelford, Cornwall. In 1766 he was given the command of HMS Dolphin to circumnavigate the world, accompanied by the Swallow under the command of Philip Carteret. The two ships were parted shortly after sailing through the Strait of Magellan, Wallis continuing to Tahiti, which he named "King George the Third's Island" in honour of the King (June 1767). Wallis himself was ill and remained in his cabin: lieutenant Tobias Furneaux was the first to set foot, hoisting a pennant and turning a turf, taking possession in the name of His Majesty. He continued to Batavia, where many of the crew died from dysentery, then via the Cape of Good Hope to England, arriving in May 1768. He was able to pass on useful information to James Cook who was due to depart shortly for the Pacific, and some of the crew from the Dolphin sailed with Cook.
In 1780 Wallis was appointed Commissioner of the Admiralty.