Dexter was born in Stamford, Lincolnshire, and was educated at Stamford School, where his brother, John Dexter, had been before him. After completing his National Service with the Royal Corps of Signals he read classics at Christ's College, Cambridge, graduating in 1953 and receiving an honorary Masters Degree in 1958.

In 1954, he started his teaching career in the East Midlands, becoming assistant classics master at Wyggeston School, Leicester. A post at Loughborough Grammar School followed, before he took up the position of senior classics teacher at Corby Grammar School, Northamptonshire, in 1959.

In 1966, he was forced by the onset of deafness to retire from teaching, and took up the post of Senior Assistant Secretary at the University of Oxford Delegacy of Local Examinations (UODLE) in Oxford — a job he held until his retirement in 1988.

Dexter featured prominently in the BBC programme "How to Solve a Cryptic Crossword" as part of the Time Shift series broadcast in November 2008 in which he recounted some of the crossword clues solved by Morse.

He started writing mysteries in 1972 during a family holiday: "We were in a little guest house halfway between Caernarfon and Pwllheli. It was a Saturday and it was raining — it's not unknown for it to rain in North Wales. The children were moaning ... I was sitting at the kitchen table with nothing else to do, and I wrote the first few paragraphs of a potential detective novel." Last Bus to Woodstock was published in 1975 and introduced the world to the character of Inspector Morse, the irascible detective whose penchants for cryptic crosswords, English literature, cask ale and Wagner reflect Dexter's own enthusiasms. Dexter's plots are notable for his use of false leads and other red herrings.

The success of the 33 episodes of the TV series Inspector Morse, produced between 1987 and 2001, brought further acclaim for Dexter. In the manner of Alfred Hitchcock, he also makes a cameo appearance in almost all episodes. More recently, his character from the Morse series, the stalwart Sgt (now Inspector) Lewis features in 12 episodes of the new ITV series Lewis. As with Morse, Dexter makes a cameo appearance in several episodes.

Dexter suggested the English poet A E Housman as his "great life" on the BBC Radio 4 programme of that name in May 2008. Dexter and Housman were both classicists who found a popular audience for another genre of writing.

Dexter has been the recipient of several Crime Writers' Association awards: two Silver Dagger for Service of All the Dead in 1979 and The Dead of Jericho in 1981; two Gold Daggers for The Wench is Dead in 1989 and The Way Through the Woods in 1992; and a Cartier Diamond Dagger for lifetime achievement in 1997. In 1996 Dexter received a Macavity Award for his short story Evans Tries an O-Level. In 1980, he was elected a member of the by-invitation-only Detection Club.

In 2000 Dexter was appointed an Officer of the Order of the British Empire for services to literature

Inspector Morse Novels

• Last Bus to Woodstock (1975)
• Last Seen Wearing (1976)
• The Silent World of Nicholas Quinn (1977)
• Service of All the Dead (1979)
• The Dead of Jericho (1981)
• The Riddle of the Third Mile (1983)
• The Secret of Annexe 3 (1986)
• The Wench is Dead (1989)
• The Jewel That Was Ours (1991)
• The Way Through the Woods (1992)
• The Daughters of Cain (1994)
• Death is Now My Neighbour (1996)
• The Remorseful Day (1999)

Novellas and short story collections

• The Inside Story (1993); Special edition, commissioned by American Express

London: Pan, Pub date 1993, Paperback, 56p.; includes crossword puzzle

• Neighbourhood Watch (1993); Limited edition of 229 copies

Richmond: Hartley Moorhouse and Geir Moe Sorenson ISBN 1898154007, Pub date May 1993, Paperback in slip case

• Morse's Greatest Mystery (1993); also published as As Good as Gold
1. "As Good as Gold" [Insp. Morse]
2. "Morse's Greatest Mystery" [Insp. Morse]
3. "Evans Tries an O-Level"
4. "Dead as a Dodo" [Insp. Morse]
5. "At the Lulu-Bar Motel"
6. "Neighbourhood Watch" [Insp. Morse]
7. "A Case of Mis-Identity" [a Sherlock Holmes pastiche]
8. "The Inside Story" [Insp. Morse]
9. "Monty's Revolver"
10. "The Carpet-Bagger"
11. "Last Call" [Insp. Morse]

Uncollected short stories

• "The Burglar" in You, The Mail on Sunday, 1994
• "The Double Crossing" in Mysterious Pleasures, ed. Martin Edwards, London: Little, Brown, 2003
• "Between the Lines" in The Detection Collection [a Detection Club volume], ed. Simon Brett, Orion, 2005.
• "The Case of the Curious Quorum" in The Verdict of Us All [a Detection Club volume], ed. Peter Lovesey, Crippen & Landru, 2006, featuring Inspector Lewis.
• "The Other Half" in The Strand Magazine, February—May, 2007.
• "Morse and the Mystery of the Drunken Driver" in Daily Mail, December 2008.

Other

• Cracking Cryptic Crosswords - a guide to solving cryptic crosswords Oxford: Offox Press ltd, 2010
• Oxford: A Cultural and Literary History Foreword by Colin Dexter, Signal Books, 2007