Wheeler was commissioned as a second lieutenant (on probation) on the General List of the Territorial Army on 13 December 1963 and, following his graduation from University, promoted to lieutenant in the Royal Ulster Rifles on 14 July 1964. He spent his early military service in Borneo and in the Middle East. He was promoted to captain on 22 December 1967 and to major on 31 December 1973 and served as a brigade major during the Cyprus Emergency in 1974. After serving on Lord Carver's staff during the Rhodesia talks in 1977, he was promoted to lieutenant colonel on 30 June 1978. He became commanding officer of 2nd Royal Irish Rangers in 1979 and led his battalion in Belize, Gibraltar, Berlin and Canada. He was then Chief of Staff in the Falkland Islands from June to December 1982 immediately following the Falklands War.