Born in Norfolk, Virginia, Tarbell was appointed midshipman in the Navy on 5 December 1798. He served in Constitution and other ships of the Mediterranean Squadron from 1800 to 1804, at the height of America's war with Tripoli. He was present, under Commodore Edward Preble's command, during the demonstration before Tripoli in 1804 and was among those honored by Congress for services rendered during that action.
From 19 to 23 June 1813, during the War of 1812, Tarbell commanded a boat expedition against the British squadron off Craney Island and in the James River. His flotilla of 15 boats fought the enemy for an hour and one-half and succeeded in forcing him to flee. In those actions, his men sank three British boats, took 43 prisoners, and killed 90 of the enemy. Tarbell was commended by his superior, Commodore Stephen Cassin, and by the army officers ashore for his gallantry and assistance in the defense of Craney Island. Just over a month later, on 24 July 1813, he was promoted to the rank of captain.
Captain Tarbell died at Norfolk, on 24 November 1815.
USS Tarbell (DD-142) was named for him.