Abell was born in Bridgnorth, Shropshire, on 11 December 1906, the son of George and Jessie Abell, his father was a Bank Manager. Abell (brother of George Abell, who became a civil servant) was educated at Repton School and Magdalen College, Oxford, though he failed to get a degree. He joined the then Colonial Administrative Service in 1929 and was posted to Nigeria. In 1942 he took part in Operation Postmaster, a successful raid on German and Italian ships in the port of Santa Isabella on Fernando Po, then a Spanish colony, although Spain was neutral in World War II. He was appointed Resident of Oyo Province in western Nigeria in 1949, but the following year he was offered the governorship of Sarawak, where he was concurrently High Commissioner to Brunei.
Abell retired in 1959 but was a member of selection boards for both the Colonial Service and the police, and was also invited to sit on the Cobbold Commission on the future of North Borneo and Sarawak. He was Gentleman Usher of the Blue Rod 1972–79.
Abell was appointed CMG in 1950 and knighted KCMG in the 1952 New Year Honours. In 1954 the Sultan of Brunei awarded him the Family Order of Brunei, First Class, "in recognition of valuable services rendered".
Abell died on 8 October 1994 in Winchester district of Hampshire aged 87.
- ABELL, Sir Anthony (Foster), Who Was Who, A & C Black, 1920–2016 (online edition, Oxford University Press, 2014)
- "Sir Anthony Abell" (obituary), The Times, London, 14 October 1994, page 23
- Fernando Po Cutting out Expedition
- Anthony Kirk-Greene, Symbol of Authority: The British District Officer in Africa (I.B. Tauris, 2006), p.116
- "No. 38853". The London Gazette. 3 March 1950. p. 1098.
- "No. 45565". The London Gazette. 4 January 1972. p. 99.
- "No. 38843". The London Gazette. 17 February 1950. p. 856.
- "No. 39421". The London Gazette (Supplement). 28 December 1951. p. 4.
- "No. 40205". The London Gazette. 15 June 1954. p. 3542.
Sir Duncan Stewart
| Governor of Sarawak
Sir Alexander Waddell
Sir Duncan Stewart
| High Commissioner to Brunei
Sir Dennis White
Sir George Beresford-Stooke
| Gentleman Usher of the Blue Rod
Sir John Moreton