Cooper was born on 17 February 1955 in Berwick-upon-Tweed. Educated at Berwick Grammar School, he then went to Royal Military College, Sandhurst, and was commissioned into the King's Own Scottish Borderers (KOSB) as a second lieutenant on 8 March 1975. He initially served in Northern Ireland, Britain and Germany, he was promoted lieutenant on 8 March 1977, and captain on 8 September 1981. In the early 1980s he served two tours with a British Army advisory and training team in Zimbabwe before attending Staff College, Camberley in 1987. He was promoted major on 30 September 1987, and after graduation from the staff course, he was appointed Chief of Staff, 8th Infantry Brigade in Northern Ireland 1988–89, for which he was appointed Member of the Order of the British Empire (MBE) on 6 November 1990. He then commanded a rifle company in 1st Battalion, KOSB (1KOSB), including active service in the Gulf War. He was promoted lieutenant colonel on 30 June 1994, and commanded 1KOSB for a further tour in Northern Ireland, for which he was appointed to the Distinguished Service Order (DSO), as well as tours in Edinburgh and Lancashire. He then served as an instructor at the Staff College, Camberley, and at the Joint Services Command and Staff College.