Yates was nominated for four Academy Awards - two as director and two as producer - for the cycling tale "Breaking Away" and the backstage drama "The Dresser."
A graduate of London's Royal Academy of Dramatic Art, Yates directed stage greats including "Dresser" star Albert Finney and Maggie Smith as well as creating one of the film world's most memorable action sequences - the much-imitated car chase in the 1968 police thriller "Bullitt."
A statement from Yates' agent, Judy Daish, said he died Sunday in London after an illness.
Born in Aldershot, southern England in 1929, Yates trained as an actor, performed in repertory theater and did a stint as a race-car driver before moving into film. He began as an editor and then became an assistant director on films including Tony Richardson's "A Taste of Honey" and J. Lee Thompson's "The Guns of Navarone."
His first film as a director was the frothy 1963 musical "Summer Holiday" starring Cliff Richard - a singer billed, optimistically, as the "British Elvis."
Yates also directed "Robbery," based on the real 1963 heist known as the "Great Train Robbery," which marked him as a talented director of action sequences.
He then went to Hollywood for "Bullitt," and went on to make well-received films including the war thriller "Murphy's War," with Peter O'Toole, and the tense crime drama "The Friends of Eddie Coyle" starring Robert Mitchum.
Nothing if not varied, his 1970s movies included crass comedy "Mother, Jugs and Speed," starring Bill Cosby and Raquel Welch, and the critically derided but commercially successful undersea thriller "The Deep."
In 1979, Yates hit another creative high with "Breaking Away," a deft coming-of-age story about a cycling-mad teenager in small-town Indiana. It was nominated for five Oscars, including best director and best picture - giving Yates two nominations, as he was also a producer on the film.
Yates received two more nominations for "The Dresser," a 1983 adaptation of Ronald Harwood's play about an aging actor and his assistant, which he directed and co-produced.
In recent years Yates had worked mostly in television. His last theatrical feature was 1999's "Curtain Call," which starred Michael Caine and Smith as a pair of theatrical ghosts.
Yates is survived by his wife, Virginia Pope, a son and a daughter.
Monday's statement said a private family funeral would be held.