He was the son of Hugh, 12th MacLean of Ardgour (1736-4 September 1768) and Elizabeth, daughter of Alexander Houston of Jordan Hill.
He entered the army as an ensign in the 2nd battalion of the Royals, in 1780, and was promoted to a lieutenancy in the same corps, from which he afterwards exchanged into the (later the 63rd (West Suffolk) Regiment of Foot).
He subsequently attained to the rank of captain and major in the 8th Regiment of Light Dragoons (later the 8th King's Royal Irish Hussars).
He was a splendid horseman and the most accomplished and daring rider in the Royal Caledonian Hunt,[3] amongst whose members was Robert Burns.
Alexander became blind several years before his death in 1855, and was buried in Cill Mhoadain Graveyard, Ardgour alongside his wife.