David Cameron welcomed the rescue package but warned swift action was needed to capitalise on the positive reaction from the markets.
A number of key details still need to be hammered out, including how to almost double the eurozone bail-out fund to one trillion euro (£880 billion).
Among those being asked to come onboard are private investors and the Chinese Government.
While there was relief that Wednesday’s summit in Brussels had produced a deal, the measures did not go as far as many experts have demanded.
Labour also warned the agreement could create a two-tier Europe, with the UK excluded from key decisions. Mr Cameron would be reduced to “receiving a postcard from Europe”, the party said.
Meanwhile, Tory back benchers reacted angrily to suggestions of a greater UK contribution to the International Monetary Fund (IMF).
Among the points agreed are that banks will have to write off half their Greek debt, at a cost of billions of pounds.
European banks have been ordered to find £100bn extra in capital by next summer, although British banks do not need extra cash holdings.
Germany and France also unveiled new moves for closer integration of budgets, taxation and sanctions for the 17 members of the single currency.
US President Barack Obama said European Union leaders had laid “a critical foundation” to solve the eurozone debt crisis with their deal.
It is the second time this year leaders have come up with a deal designed to calm market jitters affecting the entire currency.
The first agreement was judged to be a failure, in part because it took months to put in place. European leaders now face weeks of more tense negotiations to hammer out the fine detail of the latest package.
Alistair Darling, the former Labour Chancellor, was among those warning that European leaders should have made the deal months ago.
Tory Chancellor George Osborne said the eurozone now appeared to be on the “right road”, but warned the summit was not the end of the matter. He also insisted Britain would not contribute money to the specific eurozone bail-out fund -- but did concede that extra money could go to the IMF.
He stressed: “We are only prepared to see an increase in the resources the IMF makes available to all countries of the world. We would not be prepared to see IMF resources reserved only for use by the eurozone.”
On his way to a heads of Commonwealth meeting in Australia, Mr Cameron also welcomed the deal.
But he warned: “They need to keep up the momentum and work urgently to fill in the remaining detail.”
Following this week’s rebellion over Europe, both men will be concerned Tory back benchers are signalling their willingness to oppose any effort to boost Britain’s contribution to the IMF.
Under the deal European banks will have to increase the amount of cash they hold to protect against future crises to 9%. But the agreement found that there was no need for British banks to increase capital.
A second bail-out package will be agreed by the end of the year, and will include more private sector involvement.
Last night the FTSE 100 closed 3% higher as investors gave the deal their approval.
Banks led the rally, with Barclays and Royal Bank of Scotland rising 18% and 10% respectively.
What will eurozone bailout mean?
Q: Where is the money coming from?
A: That remains to be seen. Eurozone countries have put lots of money into their bailout fund. But the deal announced yesterday committed them to more than doubling its size, to 1 trillion euro. To spread the load, and the risk, they are looking for money from investors including funds and even the Chinese government.
Q: What does it mean for UK banks?
A: Unlike many of their European counterparts, UK banks do not have to increase capital. However, many are still exposed to eurozone debt, in particular to Greek and Italian debt. European banks have a deadline of June to raise nearly £100 billion in new capital.
Q: What does it mean for the UK?
A: The UK is not part of the eurozone bail-out fund, but if more money is required from the International Monetary Fund then Britain would be involved.
Q: What is a haircut?
A: That is the amount of debt that private investors, such as banks, have to write off. So far they have been asked to forego 50% of Greek debt. Many experts think it is not a high enough ratio and there was a push at the summit for it to be 60%. Even so, Greek national debt is still predicted to be 120% of GDP by 2020. Without a haircut, it would have been 180%.
Q: Will it work?
A: That also remains to be seen. The markets liked what they saw. But they need concrete and swift action in the upcoming weeks to ensure they do not lose faith.