Byron was the second son of the 4th Lord Byron. He joined the navy at a young age, accompanying Anson on his circumnavigation. In 1760 he was in command of a squadron sent to destroy the fortifications at Louisberg. In 1761, Commander Byron took possession of the Falkland Islands on the part of Great Britain on the ground of prior discovery, and his doing so was nearly the cause of a war between England and Spain, both countries having armed fleets to contest the barren sovereignty.
In 1769 he was appointed governor of Newfoundland. He was made Commander-in-chief of the British fleet in the West Indies in 1778 and 1779 during the American War of Independence. He unsuccessfully attacked a French fleet under the Comte d'Estaing at the Battle of Grenada in July 1779.
He was the grandfather of the poet Lord Byron.