tough talks ahead@
* EU leaders give formal green light
* May thanks leaders after securing new phase
* Austria warns "riddles remain" on Irish border
* Merkel says talks will be tough
* May vows orderly Brexit, sterling falls (Recasts, adds May comment, sterling)
BRUSSELS, Dec 15 (Reuters) - The European Union agreed on Friday to move Brexit talks onto trade and a transition pact but some leaders cautioned that the final year of divorce negotiations before Britain's exit could be fraught with peril.
EU leaders agreed in just 10 minutes that "sufficient progress" had been made after a deal on respective citizens' rights, the Irish border and Britain's outstanding payments, giving negotiators a mandate to move on to the main phase of talks.
"This is an important step on the road to delivering the smooth and orderly Brexit that people voted for in June of last year," Prime Minister Theresa May said outside her home in Berkshire, southern England.
"There is still more to do but we're well on the road to delivering a Brexit that will make Britain prosperous, strong and secure," May said, adding that Britain would be leaving the EU on March 29, 2019.
Summit chair Donald Tusk said the world's biggest trading bloc would start "exploratory contacts" with Britain on what London wants in a future trade relationship, as well as starting discussion on the immediate post-Brexit transition.
A transition period is crucial for investors and businesses who fear that a "cliff-edge" Brexit would disrupt trade flows and sow chaos through financial markets.
The head of the EU executive, Jean-Claude Juncker, cast May as a "tough, smart, polite and friendly negotiator". Officials said they understood the pressures on the prime minister, who leads a minority government and a deeply divided country.
NOW FOR THE HARD PART
While there was a sigh of relief that Brexit talks can move forward, EU leaders said talks on a future free trade pact will not begin until after March -- a date underlined by "guidelines" that set out how to proceed as Britain seeks to unravel more than 40 years of membership.
The talks will be tough.
"We have made good progress, the second phase of talks can start," German Chancellor Angela Merkel said. "But this will mean even tougher work - that was clear today in the discussion - than we have experienced so far."
Sterling reversed gains and fell 0.8 percent on the day to $1.3327.
Austrian Chancellor Christian Kern went further, saying even a primary school student could see that the "first phase" deal on the Irish border would come back to haunt the talks because it was impossible for Britain to leave the bloc's single market while avoiding a hard border on the island of Ireland.
"There cannot be any border controls between Northern and southern Ireland, there cannot be border controls between Northern Ireland and the UK, but there can between UK and the EU," he said.
"So our primary school students can see that there is a riddle to be solved."
In more formal language, leaders used the nine-point guidelines they agreed at the summit to support May's call for a two-year transition out of the bloc, which aims to help British business and citizens adjust to life after the European Union.
Leaders reiterated their position that Britain cannot conclude a free-trade accord with the European Union until it has left and become a "third country".
In coded language aimed at ensuring that Britain's departure will not set a precedent for others and further undermine the bloc, leaders also agreed to "ensure a balance of rights and obligations" during Britain's transition period.
Irish Prime Minister Leo Varadkar cautioned that there were "quite divergent opinions" on how a new relationship and transition would look. EU officials are unsure exactly how far Britain should continue to receive the full, unfettered economic benefits of EU membership during a transition after it leaves, even if it loses political representation in Brussels.
And before it will open trade negotiations, the EU has asked London for more detail of what it ultimately wants to achieve.
May, weakened after losing her Conservative Party's majority in a June election, has so far carried her divided government and party with her as she negotiated the first phase of talks.
But the next, more decisive phase is likely to lay bare the deep rifts among her top team of ministers over what Britain should become after Brexit.
The Dutch, traditionally British allies, said May should explain to voters just what the cost of leaving the EU's single market and customs union would mean for the economy.
"It means, for example, that the financial sector of London will have a considerable disadvantage to the position they have now," Prime Minister Mark Rutte said.
(Additional reporting by Luke Baker, Noah Barkin, Alastair Macdonald, Philip Blenkinsop and Liz Piper in Brussels; Writing by Guy Faulconbridge and Alastair Macdonald; Editing by Kevin Liffey)