EU President Donald Tusk congratulated British Prime Minister Theresa May after her 27 counterparts endorsed an interim deal on the terms of Britain's divorce, and approved the next stage of discussions.
But although talks will begin in January on a post-Brexit transition period of around two years, they stressed that actual negotiations on future trade ties would not start until March, as they need more clarity on what Britain wants.
"EU leaders agree to move on to the second phase of Brexit talks. Congratulations PM @theresa_may," EU President Donald Tusk tweeted.
May replied on Twitter, thanking Tusk and European Commission President Jean-Claude Juncker and hailing it as a major advance in the negotiations.
"Today is an important step on the road to delivering a smooth and orderly Brexit and forging our deep and special future partnership," May said.
As he arrived for the meeting on Friday, Juncker, who sealed the deal with May on December 8 after tense all-night talks, said the British premier had made "big efforts".
But he warned the next stage "would be much harder than the first phase, and the first phase was very hard".
Britain voted to leave the EU in a referendum in June 2016 and is due to end its four decade membership on March 29, 2019.
After months of difficult talks, May and Juncker agreed a deal on the key divorce issues of Britain's exit bill, the future of the Irish border and expatriate rights.
At a meeting without the British premier on Friday, the other EU leaders formally approved negotiating guidelines saying there had been "sufficient progress" in the first phase and that the second phase could begin.
May had on Thursday night addressed her counterparts over dinner and was "clear about wanting to move onto trade talks as quickly as possible" with "ambition and creativity", a British official said.
Leaders said there had been polite applause for May, who came to the summit hours after a humiliating parliamentary defeat over her Brexit plans.
After the dinner, German Chancellor Merkel said May had made "good offers" but added that "there remain many issues to be solved and we don't have much time".
Hungarian Prime Minister Viktor Orban said May was "a tough leader in the interest of Britain."
Dutch Prime Minister Mark Rutte said she was a "formidable political operator" but that it was "crucial" she sets out Britain's wish list for long-term ties.
The EU guidelines stressed that it was not possible to sign a formal trade deal until after Britain had left the bloc, and officials warned it could take years to do so.
Options for a future relationship include following the model of a recent EU-Canada trade deal, or Norway's membership of the European Economic Area.
But British officials are hoping for a deal by March on a two-year transition out of the bloc, during which their relationship would largely stay the same.
Questions still linger however over the divorce agreement, after Brexit minister David Davis appeared to suggest it was not legally enforceable and that Britain would only pay its exit bill if it got a trade deal.
There are particular concerns about the guarantee made by London, at Dublin's request, that there will be no frontier checks between Ireland and the British province of Northern Ireland.
"Even a primary school student will realize there is a problem to solve with the Irish border," said Austria's Chancellor Christian Kern.