Leo Varadkar is elected as Ireland's new Taoiseach
The Fine Gael leader was elected by 57 votes to 50, with 47 abstentions, on Tuesday.
He takes office on the 10th anniversary of first taking a seat in the Irish parliament, the Dail.
Paying tribute to his predecessor, Enda Kenny, Mr Varadkar said: "The country as we know it would not be here today if it was not for Enda Kenny."
He added: "For some, politics is a bad word but we've seen, in some countries, and in this one, that it can be a way to convince people that change is possible.
Mr Kenny, who resigned as Taoiseach earlier on Tuesday, nominated Mr Varadkar as his successor.
The 38-year-old Mr Varadkar, the right-wing son of an immigrant Indian doctor, is Ireland's youngest and first gay premier.
Mr Kenny said his successor would take control of a country in much better shape than it was six years ago, and would meet existing challenges, including Brexit and Ireland's future in the European Union, head on.
"As the country's youngest holder of this office, he speaks for a new generation of Irish women and Irish men," he said.
"He represents a modern, diverse and inclusive Ireland and speaks for them like no other, an Ireland in which each person can fulfil their potential and live their dreams."
In a drawn-out heave to replace Mr Kenny, Mr Varadkar secured the backing of a majority of the party's elected representatives earlier this month.
His rival, 44-year-old father-of-three Simon Coveney, had the hearts and minds of most of the grassroots membership and has since been appointed deputy leader.
A qualified doctor who has held three Cabinet posts, Mr Varadkar only revealed he was gay months before Ireland became the first country in the world to back same-sex marriage in a referendum in May 2015.
His parents Ashok and Miriam, and partner Matt, were among the guests in the Dail's distinguished visitors gallery for his election.
Mr Kenny announced last month he was stepping down after 15 years leading Fine Gael and six years as Taoiseach.
He had been under sustained pressure within his own ranks to allow a successor to be elected so the party is prepared for the next general election.
Questions already loom over how long the new Taoiseach - Ireland's 13th - can hold on to the office.
The administration is propped up by Fine Gael's ancient rivals Fianna Fail as part of a supply and confidence arrangement after an unprecedented schism in the electorate.