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 later on Thursday, according to a report on BBC.
Downing Street said the prime minister was currently briefing 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 £39b "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 has repeatedly made clear that agreement is needed on the future framework in order to press ahead with the legally-binding withdrawal agreement.
It is not clear whether further negotiation will be needed before, or at, Sunday's EU summit to resolve tensions over parts of the withdrawal agreement, amid complaints from some EU member states about its contents.
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.
The BBC's Brussels reporter Adam Fleming said, from a first reading of the draft document that has just been published, it contained "something for everyone" but there was "lots" in it that would need to be negotiated after Brexit day.
If all goes as planned, the UK and the EU will use the political declaration as the basis for a trade agreement, to be hammered out during a 21-month transition period that is due to kick-in after 29 March, during which the UK will continue to be a member of the EU single market and customs union.
The draft document stresses that any final deal with the UK must not interfere with the EU's "four freedoms" - the free movement of goods, services, capital and people within the remaining 27 EU nations.
It says, "The future relationship will be based on a balance of rights and obligations, taking into account the principles of each party.
"This balance must ensure the autonomy of the union's decision-making and be consistent with the union's principles, in particular with respect to the integrity of the single market and the customs union and the indivisibility of the four freedoms.
"It must also ensure the sovereignty of the United Kingdom and the protection of its internal market, while respecting the result of the 2016 referendum including with regard to the development of its independent trade policy and the ending of free movement of people between the Union and the United Kingdom."
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