Mr Kelly, who starred in numerous roles from Wanderly Wagon to Hall's pictorial weekly, is most fondly remembered for the character of Fr Jack in Father Ted.
He had suffered from Parkinson's disease in recent years and is survived by his wife Bairbre and seven children.
Rob Morgan, the son of Father Ted's Dermot Morgan, said it is poignant that Frank passed away 18 years to the day since Dermot died.
