"May he rest in peace".
Big Tom was regular visitor to Westmeath.
The Irish prime minister (taoiseach) also paid tribute saying he was very saddened to hear of the death.
A statement from his family said he died peacefully.More news: Weather Forecast: More snow today, but warmer days are near
Local, tributes were paid by Cavan-Monaghan Fianna Fail TD Niamh Smyth, who described Big Tom as an Irish "music legend and a true gentleman". He was a trail blazer in his time, travelling the length and breath of Ireland as well as the United Kingdom entertaining the huge crowds that he and his band The Mainliners drew to every venue that they played. His songs were a reflection of Irish life and an important connection for the Irish diaspora.
"Big Tom is a household name, not only in Ireland, but in many parts of the UK".
Speaking about this year's Country Music special Tubridy said: "This is the third year of our Country Specials and it has really established itself as one of the audience's favourite Late Late Shows".
"I want to extend my condolences to his family and his huge army of fans".More news: Teenager unearths treasures linked to Harald Bluetooth
Rose McBride, Shirley Jones, Big Tom who made a special appearance for the birthday girl Margo O'Donnell back in 2011..
Mr O'Donnell said: "I grew up all through Big Tom's career".
She said: "From Four Country Roads to Gentle Mother, his hits have travelled far and wide, earning him the title of the King of Country Music".
President Michael D Higgins referred to Big Tom as one of the most "charismatic and influential artists in Irish country music".More news: Microsoft Rolls Out Spring Creators Update For Windows 10
"It's just so sad", he told RTE Radio One. I am sure his family are devastated at his passing.