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 television credits include Pennies from Heaven, The Night They Raided Minsky's, and Zelig, as well as specials featuring performers such as Gene Kelly and Judy Garland. In 1952, he created the Tap Dance Concerto with composer Morton Gould.
Daniels' students include Christopher Walken.