His first wife was Jeanne Watson from Chicago, who was a clerical worker at the movie studios in the late '50s. They were married in 1960 but due to personal differences, divorced within a year of their marriage. At the time of this first marriage, Kaye had a supporting role with Elaine Stritch and Rose Marie in the CBS sitcom My Sister Eileen. His second wife, Angela Bracewell, was a former Broadway chorus girl whom he met while living in England. She was the hostess of the British version of the Beat the Clock (1950) game show, a segment of Val Parnell's Sunday Night at the London Palladium (1955). They remained wed until his death.
His home was in Rancho Mirage, California. He died at age 79 on December 14, 1997 from lung cancer in Los Angeles, California.