The two sides have also agreed a draft deal extending the transition period by one or two years beyond the end of 2020, a final sticking point of the divorce deal.
European Council President Donald Tusk said the EU executive, the European Commission, informed him it has agreed the political declaration on the future ties with Britain.
"I have just sent to EU27 a draft Political Declaration on the Future Relationship between EU and UK," said Tusk, who represents the 27 remaining EU member countries.
"The Commission President (Jean-Claude Juncker) has informed me that it has been agreed at negotiators' level and agreed in principle at political level," Tusk tweeted.
He said EU leaders still have to endorse the draft declaration, which is due to accompany a draft of agreed terms for Britain's withdrawal from the bloc on March 29.
Austria's key role
Shortly before a meeting with her Austrian counterpart - Sebastian Kurz - Theresa May described the latest development as, "the right deal for the UK that delivers on the referendum vote."
Austria currently heads the EU presidency and so Kurz is set to play a key role when EU leaders meet at a summit in Brussels on Sunday to endorse both documents.
Speaking alongside May, Kurz expressed his country's desire to maintain the unity of the EU, but warned that Spain needed reassurances about the status of the British island of Gibraltar.
Transition period extended
The other areas cover law enforcement, criminal justice, foreign policy, security and defence and wider areas of cooperation, according to the draft.
In an update of the withdrawal agreement, both sides have agreed to extend the post-Brexit transition period from December 31, 2020 "for up to one or two years."
The transition period is designed to allow governments and businesses to adjust to a new relationship after more than four decades of close ties.
Following the announcement of the draft declaration, the British parliament said Prime Minister Theresa May will make an "emergency statement" to MPs on Thursday.
Downing Street said the prime minister was holding a teleconference with cabinet ministers about the deal.
UK industries are on tenterhooks as the March 29 deadline draws closer. An extended transition period is likely to calm the nerves of the food and pharmaceutical industries.
In August the UK government recommnended that pharmaceutical companies stockpile six months worth of medication to avert shortage post-Brexit.
"The risk of a shortage of medical supplies to hospitals remains real and has yet to be addressed by the government," Martin Sawer, Director of Healthcare Distribution Association, told RFI.
Food distribution companies are also making provisions to avert post-Brexit shortages by doubling the time food is stored before being distributed.
"Some companies are now storing food for twelve days instead of five, but they cannot store food for three months," Tim Long, Vice President for Sales and Distribution at Tiger Soybeans, told RFI.