Revill was born in Wellington, New Zealand, the son of Eleanor May (née Neel) and Malet Barford Revill. He attended Rongotai College. He originally trained to be an accountant in New Zealand, but decided to change his career path in 1950 when he made his stage debut as Sebastian in Twelfth Night. He then moved to England, where he appeared in The Shakespeare Memorial Theatre Company's celebrated 1956–1958 season of productions in Stratford, which included Hamlet, Love's Labour's Lost, The Merchant of Venice, Julius Caesar and The Tempest. He went on to have such varied stage roles as Ratty in Toad of Toad Hall and Jean-Paul Marat in Marat/Sade.

He made his Broadway debut in 1952, playing Mr. Pickwick in The Pickwick Papers, and subsequently appeared in Irma La Douce, The Incomparable Max and Oliver!, for which his Fagin was nominated for a Tony Award. He is also known for his roles in the operettas of Gilbert and Sullivan, on both stage and television. He starred in the first national tour of the musical Drood, replacing George Rose, who was murdered during the run.

His red hair and distinctive Mr. Punch-like features often saw him cast as comic eccentrics in a number of British films of the 1960s and 1970s such as Kaleidoscope (1966), Modesty Blaise (1966), Fathom (1967), The Assassination Bureau (1969) and One of Our Dinosaurs Is Missing (1975). He also had notable supporting turns in Otto Preminger's Bunny Lake Is Missing (1965) opposite Laurence Olivier, and his American film debut A Fine Madness (1966), as well as a rare leading role in the horror film The Legend of Hell House (1973).

He was often cast as humorous foreign characters (he has played everything from Chinese to Russian). Two of his highest profile roles of this kind were in two films for Billy Wilder: The Private Life of Sherlock Holmes (1970) and Avanti! (1972), for which he was nominated for a Golden Globe Award for his part as put-upon hotel manager Carlo Carlucci.

He is also known for his voice work in feature-length films and animated series, which includes Alfred Pennyworth in the first three episodes of Batman: The Animated Series, the voice of Chico in the 7 episodes of Chico the Rainmaker (The Boy with the Two Heads) (1974), the voice of Emperor Palpatine/Darth Sidious in the original 1980 version of The Empire Strikes Back (he was later replaced by Ian McDiarmid in the 2004 DVD version to maintain continuity with Return of the Jedi and the Prequel trilogy, though Revill is still credited), numerous cartoons such as The Transformers, Batman: The Animated Series and DuckTales and more recently video games, including Marvel: Ultimate Alliance and Conquest: Frontier Wars.

After relocating to the United States, he guest-starred in many television series, such as Columbo (1978, "The Conspirators"), Hart to Hart, Dynasty, Magnum, P.I., The Love Boat, Remington Steele, Murder, She Wrote, Babylon 5, The Feather and Father Gang, Newhart, MacGyver, Dear John, The Fall Guy, Maude, and Star Trek: The Next Generation. He starred as the wizard Vector in the short-lived series Wizards and Warriors.