Taoiseach Leo Varadkar had what has been described as a "good call" with British Prime Minister Rishi Sunak about the restoration of the power-sharing institutions in Northern Ireland.
A statement said: "The Taoiseach and Prime Minister welcomed the developments overnight, and both leaders said they hope this paves the way for the early restoration of the Northern Ireland Executive and the Assembly, and that North-South Ministerial meetings will resume again."
The two leaders "agreed to keep in touch over the coming period".
Following the phone call, a spokeswoman for Mr Sunak said he was confident that power-sharing could be restored soon.
"The prime minister said was he was confident that the steps taken paved the way for the restoration of power sharing in the Northern Ireland executive," Mr Sunak's spokeswoman told reporters in a read out of the call.
"Both leaders agreed it was in the people of Northern Ireland's interest to have a stable, devolved government and this was also beneficial to relations between the UK and Ireland," she added.
The Taoiseach told the Dáil that it would be "very positive" if the Executive and Assembly in Northern Ireland return.
He said that, as we enter spring, such a development would bring "new hope".
It means the Stormont Executive could potentially be restored within days after a suspension of almost two years.
Earlier, Mr Varadkar welcomed the DUP move and said while there have been consultations between the European Commission and the Irish and British governments over the past few months, he has not seen the fine detail of what has been agreed.
"Obviously we'll need to see it and be confident that it doesn’t have any negative consequences for the Windsor framework or the Good Friday Agreement, I don’t anticipate that it does but we have to see the exact details first," he said.
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Speaking on RTÉ's Morning Ireland, Mr Donaldson said the details of the deal will be published by tomorrow and everyone will be able to see what has been agreed then.
Mr Varadkar said the deal will "enable the North-South bodies to function again, which is very important in terms of North-South co-operation.
"For our part, the Irish Government is very keen to work very closely with the new Executive to do all that we can do to make sure that it's successful and that it lasts because success and sustainability are really important," he said.
Tánaiste and Minister for Foreign Affairs Micheál Martin said that there will be no issue with the DUP's revised deal from an EU perspective.
He said that he hopes the Northern Ireland Assembly will be up and running "relatively quickly" as public services are "under strain".
Mr Martin said today's development is good news for Ireland, and he believes the DUP's previous concerns over divergence and future have been resolved.
He told RTÉ's News at One: "There comes a time when the opportunities that arise because of access to the European single market and the GB market should be grasped by the people and political leadership of Northern Ireland."
He said both Ireland and the EU are eager to see a government back in place, and that there are various mechanisms within the Windsor Framework to help solve any issues that might arise in future.
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In a statement, Northern Ireland Secretary Chris Heaton-Harris said that Mr Donaldson "has said this is subject to the binding commitments between the Democratic Unionist Party and the UK government - I can confirm that we will stick to this agreement.
"I now believe that all the conditions are in place for the Assembly to return, the parties entitled to form an Executive are meeting tomorrow and I hope to finalise this deal with the political parties as soon as possible."
He said that he will publish the details of proposals tomorrow, once they have been cleared during party talks today.
Speaking outside Westminster at noon he said there were "significant changes" to the Windsor Framework, but he does not believe there will be a need to renegotiate with the EU.
He said he believes all of the conditions are in place for the Assembly to return.
He confirmed the financial package worth over £3 billion offered to the government before Christmas will be made available to a new Executive.
He said issues such as public pay is down to the new government to iron out.
He added that the British government remains "completely committed" to the Good Friday Agreement.
Sinn Féin leader Mary Lou McDonald said she was optimistic that devolution will be restored before a legal deadline of 8 February, adding that there are "big, big challenges facing society".
She said: "We've been waiting some time for a positive decision. I am hugely encouraged by this development. We have some more work to do to get this over the line. But we need government in the North back urgently. People deserve that, society and the economy needs it."
Ms McDonald said she is travelling to Belfast "in a very positive space".
She said critically nothing has been agreed in any way intrudes on the Good Friday Agreement.
Ms McDonald added: "It's been a long time. It's been a long journey. And I look forward now to my friend and colleague Michelle O'Neill, taking up office and position as a First Minister for all.
"We believe in good government for everyone, and we will embrace the opportunity to deliver just that."
Traditional Unionist Voice leader Jim Allister accused the DUP of caving in on the Irish Sea border.
"Sadly, in betrayal of their own solemn pledges, the DUP has caved in on the Irish Sea Border, EU law and the suspension of Article 6.
"Seems not one word of the Union-dismantling protocol has been removed," he said.
Sinn Féin's leader in Northern Ireland, Michelle O'Neill welcomed the move and said the main parties in the North "will come together later today".
I welcome the public declaration by DUP Leader Jeffrey Donaldson that power-sharing will now be restored.
— Michelle O'Neill (@moneillsf) January 30, 2024
The parties will come together later today. We have much to do to confront the challenges facing our public services, workers and families which require urgent action.
First and Deputy First Minister will be elected this week, says Beattie
The leader of the Ulster Unionist Party leader said he believes the Stormont Assembly could be up and running by Monday next week.
Doug Beattie said he believes a First and Deputy First Minister will be elected by Thursday "at the latest" and the first official sitting day of the new executive could take place next Monday.
He said he believes the DUP and the UK government will move quickly on the issue.
"If we allow this to sit over the weekend, we could enter an arena where things could potentially unravel," he said.
Alliance party member and MLA for North Belfast Nuala McAllister said one word describes the decision by the DUP to return to power-sharing and that is "finally".
Speaking on RTÉ's Morning Ireland, she said: "There's been a lot of damage done over the last two years because of the DUP's boycott.
"Our public services are crumbling. Our economy has so many missed opportunities, other areas, such as the environment and education have been scarred. There's a lot of work to do.
"It's important that we get stuck right into it and that we ensure that the financial package that has been on offer from the UK government is taken on board, but also that we secure that additional financial package from the UK government so that we can have our sustainable finances."
The British government has pledged a financial package of £3.3bn to support a restored Executive, including almost £600m for public sector pay claims.
Minister for Justice Helen McEntee said the decision by the DUP is "really welcome".
Speaking on her way into Cabinet this morning, she said the return of the Executive "could be a matter of days and not before time".
Labour Party leader Ivana Bacik welcomed the "prospect of [an] imminent restoration of [the] Stormont Executive and power-sharing arrangements" adding that it was "long overdue".
