EU leaders have agreed to move Brexit talks on to the second phase but called for “further clarity” from the UK about its future intentions.
Talks will now move on to the long-term relationship between the UK and EU.
The first issue to be discussed, at talks next month, will be the terms of an expected two-year transition phase after the UK’s March 2019 exit.
Theresa May welcomed the move as an “important step on the road” to ensuring a “smooth and orderly” exit.
While acknowledging “very significant progress” had been made, German Chancellor Angela Merkel said the next phase would be “even tougher”.
Donald Tusk, the president of the European Council, tweeted the news that the 27 EU leaders were happy to move onto phase two after they met in Brussels.
He congratulated UK Prime Minister Mrs May on reaching what the BBC’s political editor Laura Kuenssberg said was a major moment in the Brexit process.
Mrs May has said she wants both sides to approach the next phase of negotiations, which will determine the long-term shape of the UK relations with the EU, with “creativity and ambition”.
The EU has published its guidelines for phase two of the negotiations, with discussions on future economic co-operation not likely to begin until March.
But EU members can begin internal discussions about their future relationship with the UK now, which Downing Street is understood to be pleased about.
The three page document says the UK will remain under the jurisdiction of the European Court of Justice and be required to permit freedom of movement during any transition period.
And agreements on the Irish border, the so-called divorce bill and the rights of EU and UK citizens, agreed by Mrs May last Friday, must be “respected in full and translated faithfully into legal terms as quickly as possible”.
‘End state’
The document says: “As the UK will continue to participate in the customs union and the single market during the transition, it will have to continue to comply with EU trade policy.”
On trade, it says while the EU is willing to engage in “preliminary and preparatory discussions” as part of building a “close partnership” after the UK’s departure any formal agreement “can only be finalised and concluded once the UK has become a third country”.
The document “calls on the UK to provide further clarity on its position on the framework for the future relationship”.
And in a passage added during the past week, it invites the EU’s negotiator Michel Barnier to “continue internal preparatory discussions, including on the scope of the framework for the future relationship” rather than having to wait until March.
Mr Juncker said on Friday that the EU’s initial priority was to “formalise the agreement” that had been reached before moving forward, adding “the second phase will be significantly harder and the first was very difficult”.
French President Emmanuel Macron said in moving forward the EU had maintained its unity, protected the integrity of the single market and ensured “compliance with our own rules”.
Mrs May is set to discuss her vision of the “end-state” for the UK outside the EU at a cabinet meeting on Tuesday, having suffered her first Commons Brexit defeat earlier this week.
Brexit Secretary David Davis said the government was “ready for the next stage”.