'Brendan's family wish to express their gratitude for the many messages of support and outpouring of love from his adoring and loyal fans.
The Comedian, who has strong links to Clare, having ran and pub in Killaloe and lived in the area for a number of years, passed away following a short illness.
Brendan had suffered with poor health but continued to perform and had been due to tour Ireland this summer before being diagnosed with cancer.
In the UK, Grace was probably best known for his role as Fatherr Fintan Stack in the 1996 Father Ted episode New Jack City - in which he uttered the classic line: "I've had my fun and that's all that matters".
Another person added: "Brendan Grace RIP, a lovely person, unrivalled comedian, superb singer and guitarist, our careers intertwined over the years, our sincerest condolences to Eileen and family, RIP Brendan".
"So sad at the passing of a great comedy legend, husband and father Brendan Grace". His character Bottler was a fan favourite, while his song "Combine Harvester", which was a hit in Ireland in 1975, went on to be covered by The Wurzels in 1976.
His spokesperson confirmed that he was very ill to the Irish Daily Mirror, saying "Brendan Grace has been in hospital for the last four weeks receiving treatment for pneumonia".