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.
But European Commission President Jean-Claude Juncker has warned the negotiations will be "significantly harder" from now on.
Donald Tusk, the president of the European Council, tweeted the news that the 27 EU leaders are happy to move onto phase two after they met in Brussels.