The musical is based on the classic 1975 Albert and David Maysles documentary of the same name, which followed the lives of the eccentric Edith Bouvier Beale and her daughter, Edith B. Beale Jr., distant relatives of Jackie Kennedy, who live in isolation on a seedy estate in Long Island. Grey Gardens is the name of the 28-room mansion they live in.
Wright said the show's score was being composed by Scott Frankel and Michael Korie.
Wright won the 2004 Tony Award for his play I Am My Own Wife. The play's star, Jefferson Mays, also won a Tony Award. After its Broadway run, Wife will begin a tour of the U.S, beginning in Chicago.