Nine independent TDs have voted for Mícheál Martin as Taoiseach.
It gives the new coalition 93 votes in the Dáil chamber
Members of the Regional Independents technical group largely backed the motion, although former Minister for Communications Denis Naughten was one of three abstentions across the house.
Tipperary TD Michael Lowry voted for Martin.
"'I've decided to make my contribution to stability by supporting the nomination of Mícheál Martin, and also supporting the appointment of ministers to a new government," he said.
"Mícheál Martin has the credentials to be an excellent Taoiseach and leader of our country. I wish him well, and know that he will lead in a spirit of consensus and collaboration."
Deputy Lowry's constituency rival Mattie McGrath abstained, saying he cannot support an "attack on families, the elderly, and rural Ireland".
Seán Canney, who was a minister of state as one of the independent TDs who supported the Fine Gael minority government, voted against.
"The protection of family farms, regional development, jobs for our young people, improved childcare and a stimulus package to reboot our small and medium enterprises are all issues to which I will hold the new Government accountable," he said.
Kildare South's Cathal Berry, Louth's Peter Fitzpatrick, Noel Grealish of Galway West, Michael McNamara of Clare and Sligo-Leitrim's Marian Harkin and Wexford's Verona Murphy all voted for the motion to elect the Fianna Fáil leader.
Others in the Regional Independents group are opposing the deal.
Members of the Rural Independents either voted against Martin or abstained -- including Michael and Danny Healy-Rae.
"I cannot support the programme for government because of a number of reasons.
Two members of the Independent group of six TDs, Marian Harkin and Michael McNamara, voted for Martin with the rest voting against.