Swinburn was born in Oxford. Nicknamed the "Choirboy", he rode his first winner, Paddy's Luck, on 12 July 1978 at Kempton Park but gained considerable fame for riding the superstar Shergar to victory in the Epsom Derby in 1981 by a record 10 lengths. He went on to win the Derby two more times.
In 1983, he rode All Along to victory in the Prix de l'Arc de Triomphe then the filly captured 1983 Eclipse Award for Horse of the Year honors with three straight major event wins in North America: the Washington, D.C. International at Laurel, Maryland, the Canadian International Stakes (Rothmans International) at Woodbine Racetrack in Toronto, Ontario, and the Turf Classic at Aqueduct Racetrack in Jamaica, New York. In 1996 he rode Pilsudski to victory in the Breeders' Cup Turf at Woodbine Racetrack and the Grosser Preis von Baden at Iffezheim Racecourse in Baden-Baden, Germany.
After retiring as a winner of numerous Group One races, including eight British Classics, Swinburn began working as a licensed trainer in 2004 and operates Walter Swinburn Racing Stables based at Church Farm in Aldbury, Tring, Hertfordshire.