Prime Minister Rishi Sunak has hailed his deal on post-Brexit trading arrangements for Northern Ireland as a "decisive breakthrough".
Many Conservative MPs, including those who supported Brexit, gave their backing to the agreement.
And the DUP, whose support will be key to restoring power-sharing in Northern Ireland, said there had been "significant progress".
But the party warned that "key issues of concern" remain.
DUP leader Sir Jeffrey Donaldson said his party would now study the legal text, before reaching a decision on whether to support the deal.
The party has boycotted the devolved government until its concerns over the Northern Ireland Protocol are resolved and some Tory MPs have said they will only support an agreement if it has the backing of the DUP.
Sinn Féin, which is the largest party in the Northern Ireland Assembly, welcomed the deal, although it said it still needed to examine the details.
The party's vice-president, Michelle O'Neill, repeated her call for the DUP to return to devolved government, adding: "We always said that with pragmatism, solutions could be found."
After months of negotiation and speculation surrounding a possible deal, it was finally unveiled during a day of carefully choreographed events.
Word began to emerge from inside government at around 14:00 GMT that a deal on an issue which has vexed four prime ministers had finally been done.
The PM confirmed the breakthrough soon after during a joint press conference in Windsor with European Commission President Ursula von der Leyen.
There was a notable warmth between the PM and Mrs von der Leyen as they outlined their agreement on Monday, with the EU chief referring to the prime minister as "dear Rishi" and hailing a "new chapter" of a "stronger EU-UK relationship".
She went on to have tea with King Charles at Windsor Castle. The pair were pictured smiling and chatting, but there was concern from some MPs that the meeting would draw the monarch into a contentious political issue.
As Mr Sunak travelled back to London to address the Commons, the details of the long-awaited deal were landing well with some MPs who might have been expected to cause the PM political problems.
Northern Ireland Office Minister and arch-Brexiteer Steve Baker said Mr Sunak had "pulled a blinder".
He had been considering resigning "as late as yesterday", he revealed, but added that the agreement "should be good enough for any reasonable unionists".
During a Commons debate, former Prime Minister Theresa May urged MPs to back the deal - but two other former leaders, Boris Johnson and Liz Truss, did not attend.
Number 10 will be pleased by the response from the US, where outstanding issues over the arrangements in Northern Ireland have been seen as an obstacle in any potential trade talks between London and Washington.
US President Joe Biden said the deal was "an essential step to ensuring that the hard-earned peace and progress of the Belfast/Good Friday Agreement is preserved and strengthened".
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