Scott Rudin and Roy Furman are producing the production, which will be directed by Jack O'Brien, Variety reported.
Mueller will play Julie Jordan, Henry will be Billy Bigelow and Fleming will portray Nettie Fowler.
"It's one of the greatest American scores of all time," choreographer Justin Peck told The New York Times, explaining he hopes to pay homage to the work of the show's original choreographer, Agnes De Mille, and "extend the show further into new territory."
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