Stravinsky began work on the Variations in Santa Fe, New Mexico in July 1963, and completed the composition in Hollywood, California on 28 October 1964.
Although not composed for the purpose, Stravinsky's music was twice choreographed for the New York City Ballet by George Balanchine, a first version in 1966, and a second version in 1982, both times under the title "Variations" (; ).