The three-time Tony Award winner is one of eight new names to be given the honour at a ceremony at New York's Gershwin Theatre in January (13).
Nunn made his debut in the Big Apple theatre district in 1981 with The Life and Adventures of Nicholas Nickleby, which won him his first Tony Award. He went on to enjoy success with Cats and Les Miserables.
Playwrights Christopher Durang and Paula Vogel, and performers Betty Buckley and Sam Waterston will be among the next batch of inductees.
Nunn joins fellow Brits Dame Maggie Smith and Sir Ian McKellen in the Theater Hall of Fame.