Historic day: The two leaders sat side by side at Stormont
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Ian Paisley and Gerry Adams, sitting side by side for their first news conference in Stormont, confirmed that power-sharing would begin on 8 May.
Mr Paisley said the DUP was committed to full participation in government and Mr Adams said it was a "new era".
Tony Blair said it was a very important day for the people of Northern Ireland.
The British and Irish governments had said they would shut the assembly if an executive was not agreed on Monday.
Emergency legislation will now be rushed through Parliament on Tuesday to give effect to the 8 May power-sharing deal.
Mr Adams - wearing his Easter lily to commemorate those who died in the 1916 rebellion - and Mr Paisley were sitting at one corner of a table at Stormont.
The SDLP's Mark Durkan and the UUP's Sir Reg Empey discuss events
After the meeting, Mr Paisley said: "Our goal has been to see devolution returned in a context where it can make a real, meaningful improvement in the lives of all the people of this part of the United Kingdom.
"On Saturday, the DUP executive overwhelmingly endorsed a motion committing our party to support and participate fully in government in May of this year - this is a binding resolution."
Mr Adams said he welcomed Mr Paisley's statement.
"I believe the agreement reached between Sinn Fein and the DUP - including the unequivocal commitment made by their party executive and reiterated today - to the restoration of political institutions on 8 May marks the beginning of a new era of politics on this island," he said.
Everything we have done over the last ten years has been a preparation for this moment
Tony Blair
Gerry Adams's statement Ian Paisley's statement
"The basis of the agreement between Sinn Fein and the DUP follows Ian Paisley's unequivocal and welcome commitment to support and participate fully in the political institutions on 8 May."
Prime Minister Tony Blair said it was "a very important day for the people of Northern Ireland, but also for the people and the history of these islands".
"Everything we have done over the last 10 years has been a preparation for this moment."
Irish Prime Minister Bertie Ahern said this had "the potential to transform the future of this island".
"This morning saw unprecedented and very positive developments."
Northern Ireland Secretary Peter Hain said: "When you have got both major parties saying we will deliver... that gives me confidence that this process is finally achieved."
He said people now wanted their politicians to concentrate on "bread and butter issues".
After 8 May, he said there would still be a need for a secretary of state, as well as ministers, until there was devolution in justice and policing.
Water 'reprieve'
Both Sinn Fein and the DUP have asked the British government not to issue water bills due to be sent out this week for the first time.
Until now, people in Northern Ireland have not had to pay separate charges for their water supply. But the government has moved to change this, in line with the rest of the United Kingdom.
Speaking after Mr Paisley and Mr Adams' historic news conference, SDLP leader Mark Durkan while welcoming the development, said he could not understand why devolution could not happen on Monday.
HAVE YOUR SAY Why wait six weeks? The taxpaying people of Northern Ireland are fed up with the games politicians are playing
Chris, Belfast
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An order signed by the NI secretary restarted devolution at midnight.
In the assembly election earlier this month, the DUP and Sinn Fein emerged as the two largest parties.
Chancellor Gordon Brown promised an extra £1bn if devolution was back on Monday on top of £35bn pledged by the government over four years.
The power-sharing executive will have four DUP ministers, three Sinn Fein, two UUP and one SDLP.
The Northern Ireland Assembly has been suspended since October 2002, amid allegations of an IRA spy ring at Stormont.
A subsequent court case collapsed. Direct rule has been in place since that date.
StormontFollowing an historic meeting between Ian Paisley and Gerry Adams, the leaders of the DUP and Sinn Fein respectively, devolved government is to return to Northern Ireland. A delay has been agreed by those involved and a new target date of the 8th of May has been set for the restoration of power sharing in Northern Ireland. 

The governments of Britain and Ireland had warned that the Stormont assembly would be shut down if an executive had not been agreed by today.