Rees passed away Friday night at his New York Home after a "brief illness," his publicist said.
Rees abruptly dropped out of the Broadway production of The Visit in May to undergo treatment for a medical condition. The show's producer was hopeful about welcoming Rees back to the stage, but the Kander & Ebb musical closed on June 14.
The actor is best known for playing the titular role in Nicholas Nickleby both on stage, in London and on Broadway, and on TV. He earned him a Tony, an Olivier Award and an Emmy nomination for his work in the Charles Dickens' adaption.
In addition to his long stage career, Rees recurred as the snobby, condescending Robin Colcord on Cheers and Lord John Marbury on The West Wing. He's also appeared on My So-Called Life, Grey's Anatomy, The Good Wife and Elementary. His movie credits include Robin Hood: Men in Tights, The Scorpion King, Frida, The Prestige and the 2006 Pink Panther remake.
He is survived by his husband, Rick Elice.