Griffiths spent almost four decades in radio, film, on television and on stage, and received some of his industry's top awards for his role in Alan Bennett's play "The History Boys".
The portly actor filled the screen as the lascivious Uncle Monty in the cult 1987 film 'Withnail and I'.
But younger fans will remember him for his portrayal of a much crueler avuncular figure - Harry Potter's red-faced and bullying uncle Vernon Dursley.
"Richard was by my side during two of the most important moments of my career ... 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 in a statement.
Griffiths' agent, Simon Beresford, described him as "a remarkable man and one of our greatest and best-loved actors". He said Griffiths died in hospital on Thursday.
The actor was born in Thornaby-on-Tees in Yorkshire, northern England, the son of a steelworker. Both his parents were deaf and he learned sign language to communicate with them.
After studying drama in Manchester, he worked in radio and on theatre, building a reputation as a Shakespearean clown.
He reprised his role as teacher Hector in a film of the "The History Boys" in 2006. One of his best known roles on television was a cookery-loving detective in "Pie in the Sky".
On stage, he was known for his intolerance of mobile phones ringing during performances, and halted plays several times to complain and even eject offending audience members.
Griffiths was given an OBE in 2008 and is survived by his wife Heather.
(Reporting by Belinda Goldsmith; Editing by Andrew Heavens)