Britain has welcomed the deal which saw Greece pull back from a potentially catastrophic economic collapse.
Prime Minister David Cameron said the agreement between Athens and its eurozone creditors enabling fresh bailout talks to go ahead offered the chance of stability in the single currency bloc
With his country teetering on the brink of bankruptcy, Greek prime minister Alexis Tsipras agreed to push through a draconian new austerity plan as the price of remaining in the single currency.
Following all-night talks in Brussels with the leaders of the 19-nation eurozone bloc, Mr Tsipras said he had managed to fend off the "most extreme measures" demanded by Greece's creditors.
He must now win the backing of the parliament in Athens for fresh pension, market and privatisation reforms less than two weeks after the Greek people overwhelmingly rejected further austerity in a referendum.
Mr Cameron said that it was in Britain's interest that the deal was now properly implemented.
"What's in Britain's interest is that there is stability in the eurozone and there isn't the threats of uncertainty and instability," he told reporters during a visit to RAF Coningsby.
"And I think this deal gives that sort of stability a chance. But obviously there is long way to go to put into place all the things that have been agreed."
Chancellor George Osborne told Sky News: "I think that Britain can give a cautious welcome that the eurozone has stepped back from the brink because it is pretty clear that these problems in Greece and across Europe have an impact on our economy.
"What we really want to see now is this turned into a lasting solution because this risk from Greece hangs over the whole European economy, including Britain."
Following weeks of bruising negotiations and political brinkmanship, German chancellor Angela Merkel warned that trust needed to be rebuilt between the radical left Syriza government and the rest of the group.
"Greece has a chance to return to the path of growth," she said, adding: "It will be a long road."
In London, early market reaction to the news of the agreement was muted, with the FTSE 100 Index up around 50 points.
The top flight had already rallied strongly at the end of last week on hopes that a deal could be reached. Banks were among those doing well today with Barclays up 2%.
The breakthrough, after 17 hours of tense negotiations, finally came in a meeting with Mr Tsipras, Ms Merkel, French president Francois Hollande and the president of the European Council, Donald Tusk.
"There are strict conditions to be met. Nevertheless, the decision gives Greece the chance to get back on track with the support of European partners," Mr Tusk said.
"It also avoids the social, economic and political consequences that a negative outcome would have brought."
Mr Tsipras – who was forced to accept a series of politically unpalatable measures to prevent his country crashing out of the eurozone – insisted that he had got the best deal possible.
"Greece will fight to return to growth and to reclaim its lost sovereignty," he said.
"We took the responsibility of the decision to be able to avert the harshest outcome. We managed to avert the demand to transfer Greek assets abroad, to avert the collapse of the banking system."
The agreement to begin talks on Greece's third bailout in five years allows the European Central Bank (ECB) to continue providing the emergency liquidity to the Greek banks which is keeping them from collapse.
However Mr Tsipras may pay a high price for the deal which is likely to be opposed by many on the left of his own party which was swept to power on an anti-austerity platform.
He appears to have calculated that with most Greeks determined to remain in the euro he had little choice but to accept the terms on offer.
Ukip leader Nigel Farage said the Greek parliament should vote down a deal which had been rejected by the Greek people.
"If I were a Greek politician I would vote against this deal. If I were a Greek 'no' voter I would be protesting in the streets. Mr Tsipras's position is now at stake," he said.
"This conditional deal shows that national democracy and membership of the eurozone are incompatible."
The Green MP Caroline Lucas said it was a "dark day" for anyone who believed in democracy.
"The oldest democracy in the world has been subjected to a coup," she said.
"The forces of darkness – the IMF, the eurozone and the ECB – are subjecting an already deeply impoverished country to further needless cruelty. National sovereignty has, in effect, been suspended."