Rees died at his home, his representative said.
Survivors include his husband Rick Elice, the playwright, whose credits include the "Peter Pan" prequel "Peter and the Starcatcher", which Rees co-directed, said The Hollywood Reporter.
A veteran of the London and Broadway stage, the Welch-born actor also was known for playing stuffy Englishman Robin Colcord on American sitcom "Cheers".
In late May, the Tony Award winner abruptly exited the Broadway production of the Kander & Ebb musical The Visit, in which he was starring opposite Chita Rivera.
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Rees, who spent more than two decades with the Royal Shakespeare Company, bagged the Tony for best actor in a play in 1982 for his work on the RSC production of "The Life and Adventures of Nicholas Nickleby".
The lanky Rees, known for his honeyed voice, earlier had accepted an Olivier Award for his work on the original 1980 London production, also directed by Nunn, and he picked up an Emmy nomination after Nickleby was shown on TV.
In 1982, Rees starred in Tom Stoppard's "The Real Thing in London", and from 2004-07, he served as the artistic director of the Williamstown Theatre Festival in Massachusetts.
On the big screen, Rees played the Sheriff of Rottingham in Mel Brooks' "Robin Hood: Men in Tights" (1993) and was "King Pheron in The Scorpion King" (2002).
His filmography also includes "Star 80" (1983), "Frida" (2002), "The Treatment" (2006), "The Prestige" (2006) and "The Pink Panther" (2006).
He had recurring TV roles on sitcoms "Singles", "Boston Common" and "M A N T I S", and he recently showed up on "Grey's Anatomy", "The Good Wife", "The Middle and Elementary".