A cabinet source told the BBC that the document has been agreed at a technical level by officials from both sides after intensive discussions this week.
A special cabinet meeting will be held at 14:00 GMT on Wednesday as Theresa May seeks ministers’ backing.
The PM has been meeting ministers in Downing Street for one-to-one talks on the draft agreement.
BBC political editor Laura Kuenssberg said the agreement contained a UK-wide customs “backstop” aimed at preventing new border checks in Northern Ireland.
There is no additional Northern Ireland-only backstop – but sources wouldn’t be drawn on any specific arrangements for Northern Ireland on rules and regulation within the UK-wide one, she added.
This “backstop” has proved to the most contentious part of the withdrawal negotiations, with concerns raised by Brexiteer Tories and the DUP over how it will work.
The pound surged against the dollar and the euro following the negotiations breakthrough – but analysts warned it could be short-lived, with the cabinet and Parliament yet to agree to the plans.
The EU said it would “take stock” on Wednesday, while the Irish government said negotiations were “ongoing and have not concluded”.
Leading Brexiteers, such as Boris Johnson and Jacob Rees-Mogg, immediately criticised what has been reported to be in the draft agreement, saying it would keep the UK under EU control.
Northern Ireland’s Democratic Unionist Party, which gives Theresa May vital support in key votes, said it would be a “very, very hard sell”.
But Conservative Chief Whip Julian Smith said he was “confident” it would pass when put to a crucial Commons vote, and Transport Secretary Chris Grayling called for “a little bit of calm” before the cabinet gives its verdict on Wednesday.
Both the UK and EU hope to be able to schedule a special summit of European leaders at the end of November to sign off the deal.
What’s been agreed?
The details of the draft agreement have not been published, so we don’t know the small print yet.
But it is made up of a withdrawal agreement – said to run to 500 pages – alongside a statement about what the UK and EU’s future relationship will look like.
The withdrawal agreement includes how to guarantee there will not be physical border checks reintroduced in Northern Ireland – the major sticking point in recent weeks.
Some Brexiteers fear the likely arrangement will keep the UK locked into EU trade rules for years to come in order to maintain a frictionless border.
The agreement also includes commitments over citizens’ rights after Brexit, a proposed 21-month transition period after the UK’s departure on 29 March 2019 and details of the so-called £39bn “divorce bill”.
The future relationship statement is expected to be far shorter, with the UK and the EU’s long-term trade arrangements yet to be settled.
No 10 said ministers were now being called to a special meeting to “consider the draft agreement the negotiating teams have reached in Brussels, and to decide on next steps”.
Before they do so, they will be able to read relevant “documentation”.