Walton was born in Walton-on-Thames, Surrey, England. He began his career in 1957 with the stage design for Noël Coward's Broadway production of Conversation Piece. Throughout the late 1950s and early 1960s he designed for the New York and London stage. He entered motion pictures as costume designer and visual consultant for Mary Poppins in 1964, for which he received an Oscar nomination.

Walton married his childhood sweetheart Julie Andrews in 1959, and the two had a daughter, Emma Walton Hamilton. Walton has said that he fell in love with Andrews when they were in their early teens and he saw her playing the egg in a theatre production of Humpty Dumpty. They divorced in 1967 but still remain close friends. Walton married Gen LeRoy in 1991. Walton, Andrews and their daughter have worked several times together professionally. He has illustrated several children's books written by Andrews and their daughter.

His awards include an Oscar for All That Jazz in 1980 and an Emmy for the acclaimed 1985 TV version of Death of a Salesman. He has received many Oscar, Emmy and other nominations, including BAFTA nominations for costume and set design for Murder on the Orient Express in 1975 and Oscar nominations for both costume design and set direction/art direction for the motion picture version of The Wiz in 1979. The film's star, Diana Ross chose Walton to design the stage set for her landmark 1983 Central Park concert, "For One & For All". Broadcast worldwide on the Showtime cable network, the concert special, over the course of two days, featured an on-site audience of over 1,200,000 on the park's Great Lawn.

In December 2005, for their annual birthday celebration to 'The Master', The Noël Coward Society invited Walton as the guest Celebrity to lay flowers in front of Coward's statue at New York's Gershwin Theatre, thereby commemorating the 106th birthday of Sir Noël.