Martin, who belongs to the right-liberal Fianna Fáil, was elected with a clear majority the day after the opposition blocked a vote.
The largest opposition party, Sinn Féin, obstructed the voting after government-loyal independent parliamentarians sat among the opposition. The party also protested on Thursday, now because the lower house Dáil Éireann is adjourned for two weeks.
The 64-year-old Martin will now lead a coalition government with the conservative Fine Gael, which is forced to rely on an alliance of independents to achieve a majority.
The agreement means a continuation of the rotation of the post of Taoiseach that the parties have used in recent years. Michéal Martin will govern until 2027, when Simon Harris from Fine Gael takes over. Harris was the one who governed until Thursday. No other party has held the Taoiseach role since the title was introduced in 1937.
In his speech after the election, Martin emphasized the country's relationship with the USA. In Ireland, there are fears that Donald Trump's decision to withdraw from the agreement on a global minimum corporate tax rate could negatively affect the Irish economy.
Our friendship with the USA is older than our state. It has endured because we have continued to renew our bonds of friendship built on respect and cooperation, he said according to The Irish Times.
Michéal Martin also led Ireland from 2020 to 2022.