European Union officials said there was a solid consensus that remaining smaller differences should not hold up a final deal for Sunday, as the other 27 governments go through the new paperwork.
Existing travel links by plane, train and road will also be preserved beyond the Brexit transition. It brings back control of our borders, our money and our laws.
The two sides have also agreed on a draft deal extending the transition period by one or two years beyond the end of 2020, a final sticking point of the divorce deal.
Theresa May will return to Brussels on Saturday to try and finalise the outline of the UK's post-Brexit relationship with the European Union, following talks with the Commission president Jean-Claude Juncker.
After briefing her cabinet in a hastily-arranged teleconference call, May addressed the House of Commons, saying the agreement was the "best possible deal".
Last year's European Union guidelines on the Brexit negotiations effectively gave Spain veto powers over future relations between the bloc and the British overseas territory.
"This prime minister seems to be very determined, very steely and eventually I think parliament will come around to supporting her".
After an inconclusive trip to Brussels to meet European Union chief Jean-Claude Juncker, the British prime minister said she would return on Saturday to finalise preparations for a full European Union meeting the next day.
Israel may look to punish Airbnb with special tax after settlement ban
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It says: "The future relationship will be based on a balance of rights and obligations, taking into account the principles of each party".
Outstanding issues include a Spanish threat to block the so-called political declaration over Gibraltar and problems from other states on fishing rights and future trade ties.
The UK-EU deal will create a free trade area with the EU unlike any other, May told politicians, adding the next 72 hours are crucial.
We are ready and willing to get behind the deal which is good for our businesses.
The Taoiseach added that the draft agreement reached on the withdrawal of the United Kingdom from the EU should not be seen by unionists as a threat to the union.
"If we did end up in a no-deal situation, we would find ourselves having to negotiate a no-deal deal quite soon thereafter", he said, speaking in Ireland's parliament.
But Northern Ireland's Democratic Unionist Party - whose 10 lawmakers prop up May's minority government - has begun abstaining on votes in the House of Commons as a sign of their displeasure at the deal.
Britain officially leaves the EU - the first country ever to do so - at midnight on March 29, but a Brexit deal must be agreed on in coming weeks to leave enough time for the European Parliament and the parliament in Britain to endorse it.
- Spain, N. Ireland pressure - May faces pressure from her Northern Irish allies, who oppose a deal they say weakens British sovereignty in their province, and from Spain, which warned it might oppose the accord over Gibraltar.