Burley was born in Toronto and raised in Windsor, Ontario, coming to the United States in 1943 after landing a singing lead in the Broadway musical, Diamond Horseshoe Revue. He continued to tour the United States after World War Two, performing primarily in musical comedies. It was during this time that Burley honed what would become a near-legendary repertoire of jokes.
While playing at the Hacienda Hotel in Las Vegas in 1962, Burley received a call from Golden Horseshoe Revue entertainer (and fellow Disney Legend) Wally Boag, with whom he worked as a contract player at Metro Goldwyn Mayer. A regular at the Golden Horseshoe Revue had taken ill and Boag concluded that Burley would fit the role perfectly. It was during that time that Burley recorded the voice of Michael and Boag the voice of José for the Enchanted Tiki Room.
Burley retired from the Golden Horseshoe Revue in 1987 and was named a Disney Legend soon after.