His most famous film role was as Hans Christian Andersen in the 1952 movie of the same name; the soundtrack includes the song "Inchworm," which subsequently became Kaye's signature tune. He sang "Inchworm" on The Muppet Show; Charles Aznavour also performed the song in his guest appearance during the first season.
Kaye hosted his own TV variety series from 1963 to 1967, with Harvey Korman as one of his co-stars. He was also one of the original owners of the Seattle Mariners baseball team; his group sold the franchise in 1981. He died in 1987.