She choreographed many of Hollywood's Golden Age dance routines.
Nelson first performed at Casa Manana in New York, where she danced with Van Johnson in the nightclub's revue.
She debuted on Broadway in 1938, and can be seen in 1944's classic film-noir Double Indemnity as Barton Keye's secretary, and 1961's Breakfast at Tiffany's, as Harriet at Holly Golightly's party.
She worked with stars like Gene Kelly, Judy Garland, Doris Day, Ingrid Bergman, Fred Astaire and Bette Davis.
In 2009, she published a biography, My Life Dancing with the Stars.