Livingston studied music at the University of Arizona. While there he composed his first score for a college musical. He moved to New York City in the 1930s, initially working as a pianist for dance orchestras.
From 1940s to the 1960s he had written songs for numerous films and television series, including Cinderella (1950), Bronco (1958), 77 Sunset Strip (television series, 1958), Hawaiian Eye (television series, 1959), Bourbon Street Beat (television series, 1959), Surfside 6 (television series, 1960), and the song "This is It" (for the 1960s The Bugs Bunny Show). He worked on Tin Pan Alley and co-wrote with Mack David the theme song to Casper the Friendly Ghost.
Livingston's Broadway compositions included the musical Molly and the musical revue Bright Lights of 1944, both with Mack David.
With Mack David he was nominated three times for the Academy Awards, the first time in 1951 for the song "Bibbidi-Bobbidi-Boo" from Cinderella (1950), again in 1960 for the song "The Hanging Tree" from the film of the same name (1959), and the last time for "The Ballad of Cat Ballou" (from the 1965 film Cat Ballou) in 1966.
He died of a heart condition at his home in Beverly Hills, California at age 78.
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