The production, which has previously been limited to strict performing restrictions, will for the first time feature all-new choreography from Anne Teresa De Keersmaeker. Van Hove's long-time collaboration Jan Versweyveld will design the show.
Van Hove's directing credits in London include A View from the Bridge at the Young Vic and in the West End, Hedda Gabler and Network at the National Theatre, and David Bowie musical Lazarus at the King's Cross Theatre.
Jerome Robbins, Arthur Laurents, Leonard Bernstein and Stephen Sondheim's musical is a contemporary musical reimagining of Shakespeare's Romeo and Juliet, with the American Jets and the Puerto Rican Sharks replacing the Montagues and Capulets.
The show features the songs "America", "I Feel Pretty" and "Officer Krupke".
In a statement, Sondheim said, "This is Ivo van Hove's first Broadway musical, and I'm eager to see what he does with it. What keeps theatre alive over time is reinterpretation, and when that reinterpretation is as invigorating as his productions of A View From the Bridge and The Crucible, it makes for something to look forward to with excitement."