Directed by Grandage and written by Martin McDonagh, the play will begin previews April 12 at the Cort Theatre.
Featuring a West End cast led by Daniel Radcliffe, the production will play a strictly limited run through July 20.
"Set on the remote island of Inishmaan off the west coast of Ireland, word arrives that a Hollywood film is being made on the neighboring island of Inishmore," a synopsis said. "The one person who wants to be in the film more than anybody is young Cripple Billy, if only to break away from the bitter tedium of his daily life. Martin McDonagh's comic masterpiece examines an ordinary coming of age in extraordinary circumstances and confirms his position as one of the most original Irish voices to emerge in the second half of the 20th century."
Radcliffe is best known for his work in the Harry Potter film franchise. His Broadway stage credits include "Equus" and "How to Succeed in Business Without Really Trying."