Fianna Fáil leader Micheál Martin is set to be elected taoiseach (Irish prime minister) at a special meeting of the Irish parliament later.
On Friday, members of Fianna Fáil, Fine Gael and the Green Party backed a programme for government, paving the way for an historic coalition.
Voters went to the polls in a general election in February but no party received a majority.
Coalition talks were then halted by the coronavirus pandemic.
The two larger parties needed the support of the Greens to have a working majority in the Irish parliament (the Dáil).
The party leaders and their negotiating teams reached agreement on a coalition deal earlier in June.
Fianna Fáil and Fine Gael have their origins in the Irish Civil War almost 100 years ago and have never been in coalition together.
After the deal was endorsed on Friday evening, Mr Martin described it as a “moment of opportunity and hope”.
Mr Martin is expected to be taoiseach for two and a half years and then hand the job over to Leo Varadkar, the Fine Gael leader and current caretaker taoiseach.
UK Prime Minister Boris Johnson tweeted: “Congratulations to Ireland on forming a new Government and to Micheal MartinTD on becoming Taoiseach. Ireland is our closest neighbour, good friend and ally on issues such as climate change, the global fight against Covid-19 and our shared values on human rights and democracy.”
Analysis: BBC News NI Dublin Correspondent, Shane Harrison
Micheál Martin is the only Fianna Fáil leader not to have been taoiseach, but that changes today.
He will hold the role for 30 months before handing over to Leo Varadkar, the Fine Gael leader.
The two parties, both centrist, Fianna Fáil slightly to the left and Fine Gael to the right, have dominated the politics of the state since its foundation.
Although there has been little to separate them policy-wise for decades, their decision to share power in government for the first time is historic.
But it’s also a political necessity for their leaders to keep Sinn Féin, the party that got the most votes in February’s general election, away from government.
Sinn Féin has accused the two of using the Greens as a “fig leaf” to disguise their denial of the electorate’s demand for change.
The three parties now have five years to disprove those who claim the new coalition is simply a slightly greener version of business as usual in such areas as housing and dealing with climate change in a radical manner.
A meeting between Mr Martin and Northern Ireland’s first and deputy first ministers, Arlene Foster and Michelle O’Neill, is very likely in the coming days.
While there will be new faces across the table, there will be some old problems to talk about such as Brexit and Covid-19.