Members of Fine Gael have approved the programme for government.
The vote was 80% yes to 20% no.
There were 674 votes, representing a 95% turnout of those eligible to vote.
Party leader Leo Varadkar says the vote leaves their party "united and strong" ahead of a potential third consecutive term in government.
— Leo Varadkar (@LeoVaradkar) June 26, 2020
The party is the first of three to complete their counting of votes, with results from the Greens and Fianna Fáil expected later this evening, potentially around 8pm.
Earlier, Green Party TD Roderic O’Gorman said he expects the membership of the party to approve the programme.
He suggested the vote "will be tight and the two-thirds majority that our party requires", but he was "feeling more confident" that the deal would get over the line.
If all three parties approve the deal, then the Dáil will hold a special sitting at the Convention Centre Dublin tomorrow to elect a new Taoiseach.
Under the coalition deal, Deputy Martin would hold the role until December 2022, when Leo Varadkar would take over for the remainder of the new government's term.
If approved, Micheál Martin will tomorrow also appoint his Cabinet ministers.
Sources have also said it looks as though Fine Gael will keep the Foreign Affairs, Finance, Business and Justice portfolios, while Fianna Fáil will take charge of Housing and Public Expenditure, and possibly Education.
Green leader Eamon Ryan is expected to take charge of a new Climate and Transport Department.