Prime Minister Theresa May has said the agreement with the European Commission on the draft political framework represented the "right deal" for the UK.
European Council president Donald Tusk announced on Thursday that the text had been agreed in draft form by EU and UK negotiators and "agreed in principle at political level".
The declaration outlines how trade, security and other issues will work following Brexit.
The announcement clears the way for a special Brexit summit to go ahead in Brussels on Sunday, when 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.
It follows a meeting in Brussels on Wednesday evening between Prime Minister Theresa May and European Commission president Jean-Claude Juncker, and is the first indication that the pair reached political agreement in principle on the text.
Mr 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."
Speaking outside No 10 on Thursday Mrs May said: "This is the right deal for the UK. It delivers on the vote of the referendum, it brings back control of our borders, our money and our laws and it does so while protecting jobs, protecting our security and protecting the integrity of the United Kingdom.
The Prime Minister said the draft declaration was between the UK and officials in Brussels, adding: "It is now up to the EU member states to examine this agreement in the days leading up to the special EU Council meeting on Sunday."
She added: "I will be speaking to my counterparts over that time including speaking to Chancellor Kurz of Austria here in Downing Street later today.
"Last night I spoke to the Spanish Prime Minister Pedro Sanchez and I'm confident on Sunday that we'll be able to agree a deal that delivers for the whole UK family, including Gibraltar.
"On Saturday I will return to Brussels for a further meeting with President Juncker where will discuss how to bring this process to a conclusion in the interest of all our people."
The PM finished by saying: "The British people want this to be settled, they want a good deal that sets us on course for a brighter future.
"That deal is within our grasp and I am determined to deliver on it."
According to the draft declaration agreed by the United Kingdom and the European Commission, the "parties envisage having a trading relationship on goods that is as close as possible, with a view to facilitating the ease of legitimate trade."
The draft declaration will now be screened by national envoys of the remaining 27 EU states meeting in Brussels on Thursday.
Both the EU and Britain "should aim to deliver a level of liberalisation in trade in services well beyond the parties’ WTO commitments," according to the draft declaration.
The transition period, which Britain and the EU hope will begin once Britain leaves the EU on March 29, can be extended "for up to one or two years," according to the draft declaration.
Mrs May is to make a statement to the House of Commons on Thursday afternoon on the latest developments and was speaking to members of the Cabinet in a conference call ahead of that.
She will need the backing of the House of Commons before the deal can be approved.
Her party remain split over the deal with hardline Brexiteers attempting to organise a leadership challenge against Mrs May.
The Prime Minister remains adamant that her deal is the right one for the whole of the UK.
The DUP is unhappy that the deal will see Northern Ireland aligned with EU rules and remain part of the single market with checks on some goods coming in from the UK to Northern Ireland, if the Brexit backstop is implemented.
Senior DUP figures have expressed concern that Mrs May's Brexit plan could lead to the breakup of the United Kingdom.
The Prime Minister's plan has put her confidence and supply agreement with the DUP under threat.
Mrs May currently relies on the ten DUP MPs to support her government in key votes in order to pass legislation.
Labour leader Jeremy Corbyn has said his party will be voting against Mrs May's Brexit deal, calling it a “one-way agreement” in which the EU “calls all the shots”.