And agreements on the Irish border, the so-called divorce bill and the rights of European Union and United Kingdom citizens, agreed by Mrs May last Friday, must be "respected in full and translated faithfully into legal terms as quickly as possible".
Talks on trade and security co-operation are set to follow in March.
After just a few minutes of talks, leaders of the 27 member states signed off on a three-page statement authorising the start of transition negotiations.
The UK reached agreement with the European Commission last week that "sufficient progress" had been made on so-called divorce issues, such as citizens' rights and financial liabilities, to move onto the next phase.
The EU also wants more clarity from the United Kingdom on what sort of trade and future relationship it envisages after Brexit to be able to start discussions on that future after March, when EU leaders adopt another set of guidelines for those talks.
If Wednesday's vote pointed to the battles May still faces at home over Brexit, EU President Donald Tusk acknowledged the bloc's own unity would be tested in the months ahead.
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.
"The UK and European Union have shown what can be achieved with commitment and perseverance on both sides".
The EU has said that during the transition period the United Kingdom will have to abide by EU rules and regulations as if it were member, but without a seat at the table.
During any transition, the EU is demanding that London should give up its seat at the leaders' table, lose all its lawmakers in the European Parliament and remove its judges from Europe's courts.
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But "most people in America are good people, and eventually good people will fix our country", McKinnon says. "What list is he on?" the precocious Tyler asks.
After the guidelines were adopted, May thanked her European counterparts.
"This is an important step on the road to delivering the smooth and orderly Brexit that people voted for in June 2016", she said.
The document says: "As the United Kingdom 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".
May on Thursday night had updated the leaders on the divorce deal.
"Some of us thought that she did make big efforts and this has to be recognised", EU Commission chief Jean-Claude Juncker said Friday.
But EU leaders offered their support to May.
In a brief address to fellow leaders on Thursday, Mrs May stressed her keenness to get on with shaping a "deep and special" future partnership as quickly as possible, leaving no doubt that she believes she is "on course to deliver Brexit" despite the setback of defeat in the Commons.
But he warned the next stage "would be much harder than the first phase, and the first phase was very hard".
Divergences in priorities could surface, and thus be exploited by British negotiators, although leaders seem keen to avoid that.
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.