Born in Scranton, Pennsylvania to Francis P. Burke and Rhoda Nihany, Burke grew up in Detroit, Michigan and attended St. Ambrose High School, where he was All-State fullback. After one year at the University of Detroit, playing under coach Gus Dorais, Burke transferred to Duke University, where he formed and led the jazz big band known as the Duke Ambassadors. During the 1930s and 1940s, Burke was a big band arranger in New York City, worked with Sam Donahue's band, and during the 1940s and 1950s worked as an arranger for the Charlie Spivak and Jimmy Dorsey bands, among others. In 1955, he wrote, along with Peggy Lee, the songs to Disney's Lady and the Tramp. He also wrote songs with John Elliot for Disney's Toot, Whistle, Plunk and Boom, which won the 1953 Oscar for Best Short Subject (Cartoons).
He wrote the music for number of popular songs, including "Black Coffee" and "Midnight Sun", co-written with jazz vibraphonist Lionel Hampton. The song's lyrics were added later by Johnny Mercer. Burke was an active arranger, conductor and A&R man at major Hollywood record labels, especially Decca Records where he worked with Charles "Bud" Dant. He also wrote and arranged the theme for the early 1960s show Hennesey, a jazzy update of The Sailor's Hornpipe.
Later Burke became musical director of Warner Bros. Records / Reprise Records and was responsible for many of Frank Sinatra's albums, and was producer of Sinatra's recording of "My Way" and Petula Clark's "This Is My Song" written by Charles Chaplin for his movie, A Countess From Hong Kong. He was also the bandleader for recordings of leading singers such as Dinah Shore, Bing Crosby, The Andrews Sisters, The Mills Brothers, Ella Fitzgerald, Mel Tormé and Billy Eckstine.
