The EU and UK have agreed a draft agreement on their future relationship, paving the way for a Brexit deal to be finalised this weekend.
The political declaration - outlining how trade, security and other issues will work - has been "agreed in principle", the European Council says.
London and Brussels have already agreed the draft terms of the UK's exit from the EU on 29 March 2019.
Theresa May will make a statement to MPs at 15:00 GMT.
Downing Street said the prime minister has briefed cabinet ministers on the draft agreement in a conference call.
Last week, the UK and the EU agreed a 585-page legally-binding withdrawal agreement, covering the UK's £39bn "divorce bill", citizens' rights after Brexit and the thorny issue of the Northern Ireland "backstop" - how to keep the border open if trade talks stall.
The political declaration is a separate, far shorter document, setting out broad aspirations for the kind of relationship the UK and the EU will have after Brexit, and is not legally-binding. Some of the wording of it is non-committal and allows both sides to keep their options open.
European Council President Donald Tusk said in a tweet: "I have just sent to EU27 a draft Political Declaration on the Future Relationship between EU and UK. The Commission President has informed me that it has been agreed at negotiators' level and agreed in principle at political level, subject to the endorsement of the leaders."
It follows a meeting in Brussels on Wednesday evening between Mrs May and European Commission president Jean-Claude Juncker.
Downing Street said Mrs May will return to Brussels on Saturday for further talks with Mr Juncker, on "how we can bring to a conclusion this process in the interest of all of our people".
"No final deal can be agreed without the approval of the European Council on Sunday," said the prime minister's official spokesman.
Tensions remain over some parts of the withdrawal agreement.
Spain's prime minister, 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 - and France is understood to have sought amendments to the wording on fishing rights in UK waters.
If the withdrawal agreement and the political declaration are signed off on Sunday, Theresa May will then turn her attention to getting the deal through the UK Parliament, where there is not thought to currently be a majority in favour of it.