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The political declaration - outlining how UK-EU 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.
The prime minister told MPs it would deliver the Brexit people voted for.
The political declaration is a separate document to the 585-page withdrawal agreement, published last week, which covers the UK's £39bn "divorce bill", citizens' rights after Brexit and the thorny issue of the Northern Ireland "backstop" - how to avoid the need for a manned border on the island of Ireland.
The withdrawal agreement is legally-binding - the political declaration is not.
It sets out broad aspirations for the kind of relationship the UK and the EU will have after Brexit. Some of the wording of it is non-committal and allows both sides to keep their options open.
"The negotiations (on the political declaration) are now at a critical moment and all our efforts must be focused on working with our European partners to bring this process to a final conclusion in the interests of all our people," said the PM."The British people want Brexit to be settled, they want a good deal that sets us on a course for a brighter future, and they want us to come together as a country and to move on to focus on the big issues at home, like our NHS.
"The deal that will enable us to do this is now within our grasp. In these crucial 72 hours ahead, I will do everything possible to deliver it for the British people."
But Labour Leader Jeremy Corbyn described the agreement as "26 pages of waffle" which "could have been written two years ago".
"This is the blindfold Brexit we all feared - a leap in the dark. It falls short of Labour's six tests," he added. "What on earth have the government been doing for the past two years?"
Lib Dem leader Sir Vince Cable, who is campaigning for another referendum, described it as an "agreement to have an agreement" that was "full of worryingly vague aspirations".
What happens now?
- Theresa May goes back to Brussels on Saturday for more talks with European Commission president Jean-Claude Juncker
- Negotiators try to get an agreement with Spain over Gibraltar
- EU leaders meet on Sunday to sign off on the withdrawal agreement and the political declaration
- If that is agreed Mrs May starts the process of getting MPs to back the deal - most are currently against it
- If MPs back the deal it then has to be ratified by the European Parliament
- The UK leaves the EU on 29 March - and trade talks on the future relationship start
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.
Mrs May said she had spoken to Mr Sanchez and was "confident that on Sunday we will be able to agree a deal for the whole of the United Kingdom family including Gibraltar" - and that the UK's sovereignty over the territory was not under threat.
What's new in the declaration?
- Commitment to respect the indivisibility of the EU's four freedoms - free movement of people, money, goods and services
- A specific reference to the end of free movement in the UK
- An aspiration to use technology to ensure there is no need for the Northern Ireland backstop to be used
- A clear continuing role for the European Court of Justice in the interpretation of EU law - which is likely to anger Brexiteers
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 Brexit happens on 29 March, during which the UK will continue to be a member of the EU single market and customs union.
The draft document 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."
What has the response been?
In the Commons, Mrs May faced calls from Brexiteer Conservative MPs, including former Foreign Secretary Boris Johnson, and Jeffrey Donaldson of the DUP, who have threatened to vote down the deal, to ditch the Northern Ireland "backstop" and come forward with the alternatives set out in the political declaration instead.
Opponents of Brexit were also critical of the new document.
Conservative MP Philip Lee, who quit the government in protest at its handling of Brexit, said it "reads like a letter to Santa", while Labour's Chuka Umunna, a leading supporter of the People's Vote campaign for a new referendum, said it was "entirely aspirational and doesn't finalise anything".
Scottish Conservative MPs are also concerned that the declaration will not protect the interests of the UK fishing industry.
But the government insists the UK's "red lines" on fishing have been protected, and the text acknowledges the UK will be "an independent coastal state" with the rights and responsibilities that entails.
A government source said the EU had wanted "existing reciprocal access to fishing waters and resources [to] be maintained" but this had been rejected.
The SNP's leader at Westminster, Ian Blackford, said Scotland's fishing rights had been "thrown overboard like they were discarded fish", adding, "so much for taking back control, more like trading away Scotland's interests".
Several EU countries have raised concerns about Mrs May's planned meeting with Mr Juncker on Saturday night, saying that it should not lead to any changes in the text.
Germany has reiterated that Angela Merkel would not attend Sunday's meeting if the text has not been agreed in advance.
Separately, EU diplomats have said the Spanish government "sees the making of a compromise" on the issue of Gibraltar.
