Independent Wexford TD Verona Murphy will be the next Ceann Comhairle (speaker) of Dáil Éireann.
She will become the first woman to ever hold the role after being elected by her fellow TDs (members of the Irish parliment).
Fianna Fáil's John McGuinness and Seán Ó Fearghaíl as well as Aengus Ó Snodaigh from Sinn Féin also ran for the position.
Politicians in the Republic of Ireland met for the first time since the general electio on Wednesday.
Voting to elect the 34th Dáil took place on 29 November, with Fianna Fáil, Sinn Féin and Fine Gael winning the most seats.
Fine Gael and Fianna Fáil are in negotiations with the Regional Independent group to become the third leg of the next government.
The group asked both parties to support the nomination of Murphy.
Fianna Fáil announced that they were backing their leader's endorsement of the candidacy of Murphy for Ceann Comhairle on Tuesday.
The Tánaiste (deputy prime minister) Micheál Martin backed her for the position over party candidate and outgoing Ceann Comhairle Seán Ó Fearghaíl.
Fine Gael leader Simon Harris has also recommended the party's TDs support Murphy for the position, Irish broadcaster RTÉ reported.
Mr Harris visited Aras an Uachtarain (the official residence of President Michael D Higgins) on Wednesday morning, where he submitted his resignation, although he will stay on in the role until a new taoiseach is appointed.
Proceedings in the Dáil got under way at about 10:30 local time.
The Clerk of the Dáil, Peter Finnegan, read out the names of all 174 TDs.
TDs then elected a Ceann Comhairle by secret ballot.
This election will be followed by nominations opening for the role of taoiseach, although it is not expected that anyone will be elected today as talks to form a new government have not been concluded.
If the role isn't filled, the Dáil will be suspended and a date set in the new year for members to reconvene.
The outgoing speaker, Fianna Fáil's Ó Fearghaíl told RTÉ that the role should not form part of government formation negotiations.
Speaking on RTÉ's Radio 1, Ó Fearghaíl said Martin told him that he saw the election of Murphy as being critical to the formation of a stable government.
"I am not angry, but I am deeply disappointed," Ó Fearghaíl said on Tuesday.
In her nomination speech, Murphy said politics is "the last blood sport".
"Chambers such as these are the life blood of a democracy," she said.
"We make known fears and concerns of constituents, communicate on their behalf and make known the needs of the people."
She said every member is equal, party or none.
"If elected I will uphold these simple principles," she said.
"Large numbers of people feel alienated in the electorate, removed from everyday life.
"It is incumbent on all of us to change that."
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