EU President Donald Tusk warned that talks on a post-Brexit trade deal and transition period would be even more difficult than a hard-won agreement on divorce terms that was sealed on Friday.
"Let us remember that the most difficult challenge is still ahead. We all know that breaking up is hard but breaking up and building a new relation is much harder," Mr Tusk said, reading a statement.
Issuing his draft guidelines for the talks ahead, Mr Tusk said Britain would have to follow all EU laws, including new ones, during the two-year transition period London had requested to reassure businesses and people.
He said it must respect budgetary commitments and judicial oversight during a transition in which the remaining 27 European Union member countries continue to meet and make decisions without Britain.
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Britain will also have to collect EU customs tariffs and ensure all EU checks are performed on borders with third countries, according to a copy of the nine draft guidelines obtained by AFP.
In a sign of the challenges ahead, the former Polish premier said: "We need more clarity on how the UK sees our future relations after it has left the single market and customs union.
"We are ready to start preparing a close EU-UK partnership in trade, but also in the fight against terrorism and international crime as well as security, defence and foreign policy."
Such cooperation, he said, will require the adoption of additional guidelines next year.
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Irish Prime Minister Leo Varadkar said Dublin had "achieved all that we set out to achieve" in phase one but added it would remain "vigilant" in upcoming negotiations on post-Brexit UK-EU trade ties.
"This is not the end but it is the end of the beginning and we will remain fully engaged and vigilant through phase 2," he said.
And Foreign Minister Simon Coveney said the deal "fully" protected the 1998 Good Friday peace agreement and was a "very good outcome for everyone on the island of Ireland".
Even Northern Ireland's Democratic Unionist Party, which blocked a previous version of the agreement on Monday, said it was "pleased" to see some changes which meant there would be no "red line" between Northern Ireland and the rest of Britain.
Meanwhile French Foreign Minister Jean-Yves Le Drian said the deal was "common sense".
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"I think that the work which has been done in the negotiations that were initiated by Juncker and implemented by Michel Barnier has gradually resulted in common sense," he told France Inter radio.
"We wanted the conditions of the withdrawal to be very clearly defined so that we can move to another phase and that's what's going to happen now, I hope."
Italian Minister of Economic Development Carlo Calenda hailed the move as "a major opportunity for Europe to recover" as it emerged from a "period of uncertainty".
Still, he said, Britain's exit from the EU is "a pity".
The move was also hailed in Berlin.
"It’s a step forward and now we will review the report" of the EU negotiators to see "if the conditions exist to move from phase 1 to phase 2," said Steffen Seibert, spokesman for German Chancellor Angela Merkel.
But the deal drew sharp criticism from hardliners back in the UK such as Nigel Farage, former leader of the UK Independence Party and a major driving force behind last year's Brexit referendum.
"It's not Brexit," he told BBC radio.
"A deal in Brussels is good news for Mrs May as we can now move on to the next stage of humiliation," he added on Twitter.
And campaign group Leave.EU called the agreement a "complete capitulation", saying: "Our lily-livered politicians have sold the country down the river".
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Mr Tusk said time was of the essence before Britain's scheduled withdrawal from the bloc on March 29, 2019.
"So much time has been devoted to the easiest part of the task. Now to negotiate a transition arrangement and the framework for our future relationship we have de facto less than a year," he said.
The first phase of negotiations began on June 29, about a year after Britain's shock vote to leave the bloc, and finally wrapped up when British Prime Minister Theresa May rushed to Brussels early Friday.
The European Commission, the EU executive, said it felt "sufficient progress" had been made by Britain on separation issues including the Irish border, Britain's divorce bill, and citizens' rights.
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.
Mr Tusk said he has sent the leaders the draft guidelines that they will discuss next week and urged them to mandate EU chief Brexit negotiator Michel Barnier to start exploratory talks with Britain on future ties.
Mr Barnier told a press conference that Britain's insistence on leaving the single market and customs union left the EU with no choice but to work on a post-Brexit free trade agreement modelled on the bloc's deal with Canada.
"It's not us, it's our British friends who are giving these red lines which close certain doors," Mr Barnier said.
He insisted on the EU's own red lines on preserving the integrity of the single market with its four freedoms on the movement of goods, capital, services and labour.
"Not everyone has yet well understood that there are points that are non-negotiable for the EU," Mr Barnier said.
But he also predicted continued EU-British solidarity on defence and foreign policy to ensure "ensure the stability of the continent," though it will no longer be governed by EU treaties.
He said the final version of the full withdrawal agreement will have to be completed by October 2018 - less than a year away.
