Politicians and running-mates have congratulated President-elect Michael D Higgins, who secured more than 1 million votes.
The victory came after one of the most remarkable political comebacks ever.
He seized an unprecedented 15% swing in support following the spectacular implosion of his biggest rival, independent Sean Gallagher, on live television in the final days of the campaign.
Sinn Fein's Martin McGuinness, who finished third in the poll, said: "It's been a real privilege and honour for me to stand for the presidency of my country.
"He is (Mr Higgins) is a man of great intellectual capacity and man of huge heart and I've every confidence that he will be one of Ireland's finest presidents."
Taoiseach Enda Kenny also attended the declaration and said Mr Higgins will be an outstanding President.
Tanaiste Eamon Gilmore and the Labour leader described Mr Higgins as the life, and the soul, of the party.
Outgoing President Mary McAleese said: "His success in the Presidential election marks the start of an exciting chapter for our country, our global Irish family and for the Higgins family."
Two candidates who polled poorly, Gay Mitchell of the ruling coalition party Fine Gael and independent Mary Davis, broke with protocol and did not attend the formal declaration.