The BBC confirmed his death Thursday.
Griffiths is perhaps best known for his role as Harry Potter's Uncle Vernon in the blockbuster film franchise. He also appeared opposite Potter portrayer Daniel Radcliffe in the stage production of "Equus."
"Richard was by my side during two of the most important moments of my career," Radcliffe said in a statement to TMZ. "I was proud to say I knew him."
Griffiths' other credits include the movies, "Hugo," "Guarding Tess," "Ghandi," "Withnail and I" and "Pirates of the Caribbean: On Stranger Tides," as well as the TV series "Pie in the Sky."
He won a Tony Award for his performance in the Broadway production of "The History Boys," and also starred in a film adaptation of the play.
Griffiths is survived by his wife, Heather Gibson, TMZ said.