Taoiseach Bertie Ahern, who watched the British Open, said he was delighted with Harrington's first major win.
"This is an incredible personal achievement and I am delighted for him and his family as I know how close he has come to winning a major on a number of previous occasions," said Ahern.
"I know of Padraig's dedication on the practice ground and single-minded determination to improve his golf.
"I watched the afternoon's coverage, as I know did thousands of other Irish people and enjoyed the excitement, and send my best wishes to Padraig on this fantastic victory."
Fine Gael leader Enda Kenny also sent his warmest congratulations.
Kenny, a keen golfer himself, described the victory as an historic triumph by one of Ireland's finest ever sportsmen.
"Words alone cannot capture the magnificent performance by Padraig over the last number of days. It was a remarkable display of courage and skill, no more so than in the play-off when Padraig showed true grit and talent to take the Claret Jug.
"Winning one of the majors is truly an historic achievement and the warmest congratulations go out to Padraig, as well as his wife, Caroline, and son, Patrick."
The Labour Party spokesman on sport, Jack Wall, said: "Padraig Harrington's magnificent victory in the British Open without doubt represents one of the greatest days in the history of Irish sport. Today Padraig showed his resolve, his unrivalled focus and his magnificent composure.
"My congratulations also go to Rory McIlroy, who in winning the Silver Medal proved that the future of Irish golf is in safe hands."
Members at Stackstown Golf Club were preparing to celebrate through the night.
"It is absolutely out of this world," said Tom Collins, captain at the south Dublin club.
"It's a great feeling that I have never had before. I am from Tipperary, and I've seen Tipp win an All-Ireland, but this is better.
"Having the Open winner here in Stackstown is unbelievable, out of this world, I have never experienced anything like it."
Collins said members watched the golf eagerly all day, unsure whether Harrington would clinch the championship.
"We didn't know looking at it if he was going to win," he said.
"Golf is very unpredictable. But he came out at the right end of it and done well and won it. It's great.
"We will be staying here for the rest of the night to celebrate."
As the champagne flowed, the club captain paid tribute to the player who has never forgotten his roots.
"Padraig has been here since he was 10 or 11 years of age and he is a honorary member of Stackstown," continued Collins.
"He has been associated with Stackstown all his life. He does corporate days for us and looks after us.
"We will definitely be having a big night for him when he gets back."
Meanwhile, Michael Diver, a long-term member of Holywood Golf Club, where McIlroy honed his skills, said: "All the members are over the moon, he has been playing very well lately.
"I would say there will be a few of the members who have won money on him."