Daniels was a featured dancer in several 1940s Broadway musicals, including Billion Dollar Baby, Street Scene, and Kiss Me, Kate; although he continued performing during the 1950s and after, including a tour with the Agnes de Mille Dance Theatre, Daniels quickly moved into choreography for stage, film, and television. He won a Tony Award and an Astaire Award in 1984 for The Tap Dance Kid and received three more Tony nominations for High Spirits, Walking Happy, and the 1967 revival of Annie Get Your Gun. Notable film and TV credits include Pennies from Heaven (1981), Indiana Jones and the Temple of Doom (1984), The Night They Raided Minsky's (1968), and Zelig (1983), The Judy Garland Show (1963), as well as specials featuring performers such as Gene Kelly and Danny Kaye. In 1952, he created the Tap Dance Concerto with composer Morton Gould. He choreographed the dance sequences and dubbed the tap sound effects for the movie musical Stepping Out (1991) starring Liza Minnelli.
Daniels' students included Christopher Walken.