Griffiths died Thursday at University Hospital in Coventry, central England, from complications following heart surgery, his agent, Simon Beresford, said. He was 65.
Harry Potter star Daniel Radcliffe paid tribute to the actor Friday, saying that "any room he walked into was made twice as funny and twice as clever just by his presence."
"I am proud to say I knew him," Radcliffe said.
Griffiths was born in northeast England's Thornaby-on-Tees in 1947 to parents who were deaf and mute - an experience he and his directors felt contributed to his exceptional ability to listen and to communicate physically.
"The first language he learned was sign. And therefore his ability to listen to people with his eyes as well as his ears is incredible," Thea Sharrock, who directed Equus, told The Associated Press in 2008.
Griffiths left school at 15 but later studied drama and spent a decade with the Royal Shakespeare Company, making a specialty of comic parts such as the buffoonish knight Falstaff.