The UK and EU have agreed a draft text of the political declaration on their future relationship.
European Council president Donald Tusk said on Thursday morning the statement had been approved by negotiators and “in principle” at a political level.
The announcement clears the way for a special Brexit summit to go ahead in Brussels on Sunday.
Leaders of the 27 remaining EU states are expected to give their stamp of approval to the declaration alongside the 585-page withdrawal agreement setting out the terms of the UK’s departure.
Theresa May is due to make a statement to the House of Commons this afternoon.
Labour leader Jeremy Corbyn cancelled a visit to a West Wales creamery to rush back to parliament.
It follows a meeting in Brussels on Wednesday evening between the Prime Minister and European Commission president Jean-Claude Juncker.
Downing Street has repeatedly made clear that agreement is needed on the future framework – setting out aspirations in areas like trade and security co-operation and believed to run to a few dozen pages – in order to press ahead with the legally-binding withdrawal agreement.
There was speculation that the Prime Minister was struggling to keep her Brexit deal alive, after she announced following her meeting with Juncker that she would return to Brussels on Saturday for further talks.
May said after the meeting that she and the Commission president had given “sufficient direction” to negotiators for work to begin “immediately” on resolving remaining issues.
It is believed that negotiators worked through the night to produce Thursday morning’s breakthrough.
The new text was dismissed by Scottish First Minister Nicola Sturgeon as “lots of unicorns taking the place of facts about the future relationship”.
“Fair play to the EU for pushing it as far as possible, but it adds up to a blindfold Brexit,” said Ms Sturgeon.
“Difficult issues unresolved – so extended transition/backstop almost certain.
It remains unclear whether further negotiation will be needed on Sunday to resolve tensions over elements of the separate withdrawal agreement, or whether the summit will be a simple rubber-stamping exercise
The PM has faced a strong pushback from Spain over the status of Gibraltar in the “divorce deal”, while France is understood to have sought amendments to wording on fishing rights in UK waters.
Spanish PM Pedro Sanchez has said his government is “annoyed” that the divorce agreement does not specify that Gibraltar’s future must be decided directly by officials in Madrid and London.
He insists that the issue is a bilateral matter and has threatened that Spain could vote against the withdrawal agreement unless its interests are taken into account.