Dublin-born Kelly, who played the one-armed Irish kitchen hand Albert Riddle in Robin's Nest, also played the feckless builder Mr O'Reilly in Fawlty Towers but may be best remembered for riding a motorbike naked in the comedy Waking Ned, BBC reports.
He earned a Screen Actors' Guild nomination for the 1998 film.
In 2005, he was seen by cinema audiences as Grandpa Joe Bucket in Tim Burton's adaptation of Roald Dahl's Charlie and the Chocolate Factory, opposite Johnny Depp.
Kelly was married to actor Laurie Morton and had two children.
His friend, Ballykissangel star Niall Toibin, told the Press Association: "He was a hilarious man. He had an outlook on life that was slightly skewed and made you laugh all the time."
He praised Kelly's "wicked sense of humour".
