In a show of togetherness the 27 leaders agreed the negotiating guidelines within minutes and applauded as they met in Brussels without British Prime Minister Theresa May.
EU President Donald Tusk hailed the "outstanding unity" in an often fractious club, saying it was a "firm and fair political mandate" for the Brexit negotiations.
"After four minutes we were ready, it's very promising," former Polish premier Tusk told a news conference.
Britain swiftly warned that the talks could be "confrontational".
The summit was the first since May one month ago formally triggered the two-year process of untangling Britain from the European Union after four decades of membership.
The EU guidelines say talks on a future relationship with Britain can only start once London agrees divorce terms on citizens' rights, its exit bill and the border in Northern Ireland.
But Tusk said the fate of three million EU nationals living in Britain and one million Britons on the continent was the number one priority.
"We need a serious British response," Tusk said."I want to assure you that as soon as Britain gives real guarantees for our citizens, we will find a solution rapidly."
- 'Underestimate difficulties' -
European Commission head Jean-Claude Juncker said May had repeatedly urged him to be "patient" when they had dinner in London this week, but said Britain now needed to get serious on the issue.
"I have the impression sometimes that our British friends, not all of them, do underestimate the technical difficulties we have to face," the former Luxembourg premier said.
Brexit has offered the EU a fresh chance at unity after years of bitter internal divisions over the eurozone debt crisis and migration, plus growing euroscepticism.
May, who has called elections in Britain in June in a bid to shore up her mandate for negotiations, this week accused the EU 27 of ganging up on London.
Her comments were partly in response to German Chancellor Angela Merkel, who said Britain had "illusions" about the talks.
Britain's Brexit minister David Davis said while London wanted good relations with the EU, the talks were "the most complex the UK has faced in our lifetimes. They will be tough and, at times even confrontational."
But Merkel insisted on Saturday that "no one is allied" against London and that the EU was merely protecting its interests following Britain's historic vote to leave last June.
Merkel said the 27 leaders had given a round of applause after "very quickly" adopting the guidelines.
French President Francois Hollande meanwhile praised their common position and said there would "inevitably be a price and a cost for Britain."
The EU 27 have considerably toughened the Brexit strategy since Tusk first unveiled it a month ago.
The guidelines say that trade talks can begin only when EU leaders unanimously decide "sufficient progress" has been made on divorce issues.
Merkel said EU Brexit negotiator Michel Barnier told the leaders he hoped for agreement on the divorce phase by autumn, so the talks can move onto a trade deal.
However, Britain says it wants to discuss the divorce and a trade deal in parallel.
- 40-60 billion euro bill -
In a further move that will rile London, the EU 27 also backed automatic membership for Northern Ireland if it reunifies with Ireland, and called for Spain to have a say over any deal that affects Gibraltar.
Spanish Prime Minister Mariano Rajoy insisted he had "no red lines" on Gibraltar, a rocky outcrop off southern Spain that has been a British territory for 300 years.
The leaders discussed for the first time the spoils of Brexit -- the relocation of EU medical and banking agencies currently based in London.
While the EU says citizens' rights is a priority, the most touchy issue of all is likely to be Britain's exit bill.
Luxembourg Prime Minister Xavier Bettel said this was estimated at 40-60 billion euros ($42-65 billion), which mainly covers financial commitments made by the bloc while Britain was a member.
The bill is politically toxic for May in election campaign season.
But it also risks causing divisions among EU states -- split between those that make an overall contribution, and those that are net recipients -- as they debate how to plug any holes in the EU's budget.
"There are some who don't want to pay more and those who don't want to receive less. That is going to be a real debate," Juncker said.
Actual Brexit negotiations are not expected to begin until after the British election, although the EU is set to give an official mandate to Barnier on May 22.