The award-winning performer, who appeared as Uncle Monty in cult classic Withnail & I and Uncle Vernon Dursley in the Harry Potter films, was hailed as one of the greatest and most loved British actors by a string of his co-stars and colleagues.
His unexpected death on Thursday, at the University Hospital of Coventry and Warwickshire, came at the age of 65 and followed a stellar career which drew him plaudits on both sides of the Atlantic.
Alongside his Withnail and Harry Potter roles, he was best known for the part of inspirational teacher Hector in Alan Bennett's The History Boys – which earned him a Laurence Olivier and a Tony award.
He was awarded an OBE for services to drama in 2007.
Daniel Radcliffe, who performed alongside him in the Harry Potter films and the stage play Equus, led tributes to Griffiths, whose "encouragement, tutelage and humour" made work "a joy".
Sir Nicholas Hytner, director of the National Theatre, said his death would devastate his "army of friends".
The director, who worked with Griffiths in The History Boys and The Habit Of Art, said: "Richard Griffiths wasn't only one of the most loved and recognisable British actors – he was also one of the very greatest."
Richard E Grant, who played alongside him in Withnail & I, wrote on Twitter: "Chin-Chin my dear friend."