The new adaptation will have music from Tony and Oscar-winner Alan Menken, reported Entertainment Weekly.
"A Bronx Tale" is based on Chazz Palminteri's one-man show, which first played in Los Angeles in 1990, followed by an off-Broadway run in New York (and a Broadway revival in 2007).
It focuses on an Italian-American teenager in the turbulent 1960s, who must chose between his father and a mob boss father figure.
A film adaptation came out in 1993, directed by De Niro, 71, and starring him as the teen's father, with Palminteri as the gangster.
