The agreement paves the way for EU leaders at a summit on December 14-15 to open the second phase of Brexit negotiations, covering trade talks and a transition period.
Britain voted in June 2016 to become the first state to leave the EU, after more than four decades of membership, but the talks have been slow moving and often acrimonious so far.
"The Commission is satisfied that sufficient progress has been achieved in each of the three priority areas," the European Commission said in a statement.
Negotiators worked through the night to seal an agreement on the terms of Britain's departure from the bloc.
The EU had set a deadline of Sunday after the last talks on Monday broke down when May's Northern Irish allies objected to terms for future arrangements for the Irish border.