Green leader Eamon Ryan has said there is a "sense of responsibility" now on his party after 76% of members who voted backed the government deal with Fine Gael and Fianna Fail, paving the way for the new coalition.
Some 76% of members voted yes and 24% voted no, meaning the two thirds threshold needed was reached.
A special sitting of the Dail will proceed today in Dublin's convention centre, where Fianna Fail leader Micheal Martin will be voted in as the new Taoiseach.
The approval came after Fine Gael and Fianna Fail members earlier also gave their backing.
Speaking after the historic vote, Mr Ryan said there was a sense of responsibility” on the party now and it had “a job to do”
He pledged that the Greens would work with their coalition partners as well as the Opposition in the Dail, to tackle issues such as sustaining the environment.
“Without stable nature, there is no security for any of us,” said Mr Ryan
Deputy leader Catherine Martin said that some members would be "disappointed" with the outcome. The total valid poll was 1,892, with 1,435 members voting yes and 457 voting no.
She said the goal of the Greens in government would be the “implementation of policies”.
“We will work every day to ensure this programme for government works for everyone.”
Fianna Fáil voted to approve the deal by a margin of 74% to 26%.
The resounding margin was far above what some had predicted, with fears early on Friday that the party's membership would be narrowly split on the deal. In the end, 8,194 members of the 11,000 ballots voted in favour of the coalition with the Green Party and Fine Gael.
Only one constituency - Galway West - voted against the deal, with the home of longtime opponent to the coalition Eamon Ó Cuív voting 235-131 against the deal. Party leader Michéal Martin's constituency of Cork South Central voted 94% in favour of the programme, with just eight members against.
Mr Martin said that the engagement in the "unique and historic exercise" was "very energetic".
"Democracy in our party is alive and well. I am delighted that the Programme for Government has been so overwhelmingly endorsed. I am grateful to the members for that. I am anxious we get on with the business of government."
Mr Martin said that he had not personally thought about the prospect of becoming the first Cork-born Taoiseach since Jack Lynch.
Fine Gael members voted in favour of the deal, 80% to 20%. Up to 674 votes were received in the special delegate conference, a 95% turnout.
All four sections of the electoral college in Fine Gael voted for the deal: A result that Fine Gael president Leo Varadkar said he "wasn't entirely sure" he'd win, and said it was a strong mandate for entering government.
"As president of Fine Gael I'm pleased to confirm that my party has voted 80% to 20% in favour of joining the coalition, all sections of the party, parliamentarians, national executive and constituencies voted in favour," he said.
"So Fine Gael is going to enter a third term in government and this new coalition united and strong, and we're looking forward to helping get the country through the Covid emergency, getting people back to work, businesses open and pursuing some of the reforms we got started in the last couple of years."
Mr Varadkar said he would be phoning colleagues to inform them of Cabinet positions on Saturday.