A statement from Yates' agent, Judy Daish, said he died Sunday in London after an illness.
Yates was nominated for four Academy Awards - two as director and two as producer - for cycling tale "Breaking Away" and backstage drama "The Dresser."
A graduate of London's Royal Academy of Dramatic Art who directed stage greats including "Dresser" star Albert Finney and Maggie Smith, Yates also created one of film's most memorable action sequences - the much-imitated car chase in the 1968 police thriller "Bullitt."
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, first as an editor and then as 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."
Also in Britain he directed "Robbery," based on a real 1963 heist known as the "Great Train Robbery," which marked him as a talented director of action sequences.
He 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 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 Maggie 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.