After briefing her cabinet in a teleconference call, May addressed the House of Commons, saying it was the "best possible deal".
In a tweet earlier Thursday, EU Council President Donald Tusk - who is set to chair Sunday's summit - confirmed that a draft political declaration on future ties "has been agreed at negotiators' level and agreed in principle at political level".
Britain's Supreme Court this week rejected a last ditch bid by the British government to stop Europe's top court from considering a case which seeks to determine whether London can unilaterally reverse Brexit, writes Michael Holden.
The organisation said: "Given that unique cross-border perspective, we campaigned against Brexit".
Labour leader Jeremy Corbyn described it as 26 pages of "waffle", although his own position on post-Brexit relations is scarcely more credible than May's.
On Friday, Spanish Secretary of State for the European Union Luis Marco Aguiriano said his government wanted a commitment in writing from the United Kingdom on clarifications on the status of Gibraltar in the Brexit agreement, so it would not have to vote against the final deal.
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At first, Obama was skeptical - "So, you want me to just look at those cards and read what you've said?" she asked - but she quickly came around to the bit.
"If we had a no deal we'd find ourselves having to find a deal very quickly, so why put our countries and people through that when we have a deal on the table?" he asked.
May is due to travel to Brussels on Saturday for further Brexit meetings, including with Commission President Jean-Claude Juncker, a day before a summit of the EU's 27 other leaders at which both the political declaration on post-Brexit relations as well as the divorce agreement, which alone has legal status, are expected to be formally signed off.
First, the texts must be cleared by a meeting of top European Union diplomats - the summit's so-called "sherpas" - on Friday.
The two sides commit to "an ambitious, broad, deep and flexible partnership across trade and economic cooperation, law enforcement and criminal justice, foreign policy, security and defense and wider areas of cooperation".
With just two years to go until the end of the Brexit transition period, HMRC has said its preparations for a Northern Ireland backstop could take up to 30 months - once Whitehall has said how the mechanism will work.
Spain's EU Affairs State Secretary, Luis Marco Aguiriano, said there was still time to "legally clarify" the agreement before Sunday.
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Preparations for a summit to endorse Britain's deal to quit the European Union risked running aground on the rock of Gibraltar on Friday, as Spain defended its veto over the fate of the tiny territory.
"Northern Ireland will be in the European Union customs territory while Great Britain will not".
Mr Cairns praised the prime minister's "resilience and determination to get a deal that works for every part of the country as well as bringing the country together".
"I will be pleasantly surprised if the political declaration, when it is completed, gives us that level of certainty", he said.
Northern Ireland's Democratic Unionist Party (DUP), on whom May's Conservatives depend for their majority, has been flexing its muscles, fearing that efforts to avoid a hard border with Ireland will lead to the province drifting apart from the rest of the UK.
May also added that the sovereignty of British-territory Gibraltar would be protected.
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