Fine Gael leader Leo Varadkar was appointed as Taoiseach today for the second time by President Michael D Higgins.
Mr Varadkar replaces Fianna Fáil's Micheál Martin who tendered his resignation this morning under the terms of the coalition deal struck between the parties in 2020.
The official event at Áras an Uachtaráin took place a short time after the Dáil voted in a special sitting to elect Mr Varadkar as Taoiseach by 87 votes to 62.
Mr Varadkar said that "a number of pressing challenges" will define the new administration.
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On housing, the Fine Gael leader said he will do "whatever it takes to solve this social crisis" and apply "the same spirit of determination, action and immediacy" as was applied during Covid, and all options will be considered.
The next challenge is inflation and bringing the cost of living under control, he said.
He expressed a hope to make Ireland the best country in Europe to be a child. The Department of the Taoiseach will now have a special unit to try to make this happen.
Earlier after receiving the seals from the President today, the Taoiseach said: "I'm honoured and privileged to have the opportunity to serve again.
"And I look forward to getting down to the hard work in the next few hours."
After receiving a standing ovation from TDs on the government benches when his nomination was confirmed, Mr Varadkar commended Mr Martin "on the leadership he has shown as Taoiseach, for putting the country before politics, and for providing reassurance and hope during difficult times".
He added: "In 2020 the new Taoiseach was unable to have his wife and family with him in the Convention Centre as he received the greatest honour of his life. That, too, was leadership. I am glad they are here today.
"During the pandemic we saw the best of each other, and it meant that the new coalition was born in a spirit of togetherness and hope.
"I intend for that spirit to continue as we implement, with our partners in the Green Party, the agreed Programme for Government."
Taoiseach @LeoVaradkar receives his seal of office and government seal of office from @PresidentIRL He is now officially appointed. #rtenews pic.twitter.com/Futw0Bo0mM
— Joe Mag Raollaigh (@joemagraollaigh) December 17, 2022
Mr Varadkar made reference to the foundation of the State 100 years ago as he vowed to deliver for the country's citizens.
"As Taoiseach my mission will be to build on the achievement of 100 years ago, and to work on what needs to be done for this generation and the next," he said.
"Providing hope and housing, economic opportunities and a fair start for all.
"And so I accept this nomination by the Dáil with humility and resolve, with a burning desire to make good the promise of 100 years ago and to provide new hope and new opportunities for all of our citizens."
The changing of roles at the top of Government is in keeping with the agreement underpinning the coalition.
Mr Martin was accompanied by his wife Mary when he tendered his resignation at Áras an Uachtaráin this morning, paving the way for Mr Varadkar to succeed him.

Speaking during the special Dáil sitting afterwards, Mr Martin called for new bridges to be built across society.
He said it has been "the honour of a lifetime" to serve the public as taoiseach.
He said: "It is both a privilege and a responsibility to serve as head of government in a free and democratic republic.
"I have been deeply conscious of this every day I have held the office of taoiseach. I have sought always to work on behalf of all the Irish people and not just those who support my party and our colleagues in Government."
In his speech, Mr Martin urged the defence of democracy amid rising populism. He expressed concern about the tone of political discourse in recent years, saying that we "unfortunately live in an increasingly polarised world".
Mr Martin also delivered a robust defence of the European Union during his speech and also sharply condemned the Russian invasion of Ukraine.
He paid tribute to Irish people who have welcomed thousands of Ukrainian refugees to Ireland.
Mr Martin received a standing ovation from a majority of TDs in the chamber after his speech.
Two of Mr Varadkar's Fine Gael colleagues then proposed and seconded a motion nominating him as taoiseach.
Mr Varadkar's parents, Miriam and Ashok, and his partner, Matthew Barrett, were among those who watched from the gallery. They later joined him at Áras an Uachtaráin when his appointment was formally confirmed.

During the Dáil session, parties were given an opportunity to comment on the motion. Mr Martin paid tribute to his one-time fierce political rival.
"I want to thank him [Leo Varadkar] for his co-operation over the last two and a half years and his dedicated work," he said.
"The Government has worked on the many enormous pressures but we've succeeded in keeping our focus on moving our country forward. I look forward to maintaining this spirit during the rest of our term."
When Mr Varadkar's nomination was confirmed, he returned the compliment to Mr Martin.
"I want to take this opportunity to commend Micheál Martin on the leadership he has shown as taoiseach, for putting the country before politics, and for providing reassurance and hope during difficult times," he said.
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Setting aside almost a century of animosity, Fianna Fáil and Fine Gael, two parties forged out of the Civil War of the 1920s, agreed to share power in 2020 after that year's inconclusive general election result. The Green Party also joined the coalition.
While Fianna Fail emerged from the 2020 poll narrowly winning the most seats (38), Sinn Féin (which won 37 seats) secured the most first preference votes
Sinn Féin president Mary Lou McDonald criticised the Government's record as she opposed the nomination of Mr Varadkar during today's Dáil exchanges.

She said the resignation of Mr Martin should trigger a general election as she accused the coalition of being "out of touch, out of ideas and out of time".
"We should now have a general election because we need a change of government," she said.
Ms McDonald questioned the outgoing taoiseach's claim the Government is delivering.
"Well, the rest of us must live in a very different Ireland from you," she said.
"We live in an Ireland where, during your time leading government, the housing emergency has gotten worse, where the crisis in health has gotten worse, where households struggle to get by."
No major changes in Cabinet reshuffle
Mr Varadkar previously served as taoiseach from 2017 to 2020 at the head of a minority Fine Gael administration which relied on a confidence and supply arrangement with Fianna Fáil to maintain power.
Today's mid-term switch of taoisigh also prompted a Cabinet reshuffle.
Michael McGrath will take on the Finance portfolio with Paschal Donohoe taking over the Department of Public Expenditure, NDP Delivery and Reform.
Additional reporting PA