The New York State Theater was built with funds from the State of New York as part of New York State's cultural participation in the 1964–1965 World's Fair. The theater was designed by architect Philip Johnson and opened on April 23, 1964. After the Fair, the State transferred ownership of the theater to the City of New York.
The theater is home to the New York City Ballet, and was the former home of the New York City Opera. Along with the opera and ballet, an early tenant of the theater was the Music Theater of Lincoln Center. Richard Rodgers was its president, and during his tenure many classic Broadway musicals were revived there in the 1960s. Among them were The King and I, Carousel (with its original star, John Raitt), Annie Get Your Gun (with its original star, Ethel Merman), Show Boat, and South Pacific.
In July 2008, philanthropist David H. Koch pledged to provide $100 million over the next 10 years for the purpose of renovating the theater and providing for an operating and maintenance endowment. It was renamed the David H. Koch Theater at the New York City Ballet Winter gala, Tuesday, November 25, of that year.