Enda Kenny has been elected Taoiseach, with 59 votes in favour and 49 votes against, in the fourth Dáil vote since the General Election.
The new Cabinet was announced this evening. Frances Fitzgerald was named the new Tánaiste and the new Government Chief Whip is Regina Doherty.
Michael Noonan will remain as Minister for Finance; former Minister for Health Leo Varadkar will move to the Department of Social Protection, and Simon Harris will take over the health portfolio.
Minister for Education is the new Richard Bruton and Simon Coveney becomes the Minister for Housing.
Fine Gael's first leader to be re-elected as Taoiseach thanked the 32nd Dáil for the trust it had placed in him.
His election today, he said, was in very different circumstances to five years ago when the country was in crisis.
Mr Kenny said he was leading a very different kind of Government - almost unprecedented.
The Taoiseach said everyone must work together in the best interest of all the people.
He said a significant number of TDs in the House are willing to try to make the current arrangement work in the interest of the country.
Mr Kenny then suspended the House to allow him to travel to see the President.
President Michael D Higgins signed the 'Warrant of Appointment' and Mr Kenny was officially re-appointed as Taoiseach for a second term.
As the nomination process began in the Dáil this afternoon, Independent Alliance TDs and Fine Gael ministers Simon Coveney and Michael Noonan were still locked in talks.
Mr Kenny needed the votes of the Independent Alliance to get over the line, and the last-minute obstacles were said to involve a turf-cutting issue and ministerial appointments.
Michael Fitzmaurice, Noel Grealish, Michael Healy-Rae and Maureen O'Sullivan abstained in the vote.
In the Dáil chamber this morning, Fine Gael's Noel Rock joked "fourth time's a charm" as once again he nominated Mr Kenny for the role of taoiseach.
Outgoing Tánaiste Joan Burton said the Labour Party would vote against the election of Mr Kenny as taoiseach.
She said that going forward, Labour would support proposals, on a case-by-case basis, as they see fit.
Fianna Fáil leader Micheál Martin said the arrangement reached with Fine Gael would see his party actively scrutinise the work of ministers.
He said today marks a decisive shift away from a government that controls parliament.
The new Dáil, he said, will provide a space for the debate of measures rather than the usual "punch and judy" politics.
Sinn Féin President Gerry Adams said that the Fine Gael-Fianna Fáil talks were a "masterclass in waffle and bluster".
Former Minister for Education, Jan O'Sullivan, told the Dáil tonight: "I fear we now have an administration that will be crippled by procrastination, weakness and division."
"I along with my colleagues in the Labour Party will offer constructive opposition.
"Given the events earlier today, I for one have had enough of grandstanding, brinkmanship and spin.
"I look forward to moving on from that and advocating, supporting and advancing progressive policy choices that will make our country a fairer more equal republic for all of its children."