Emergency measures worth 750bn euros ($975bn; £650bn) have been agreed to prevent the Greek debt crisis from affecting other eurozone countries.
The 16 members of the single currency bloc will have access to 440bn euros of loan guarantees and 60bn euros of emergency European Commission funding.
The International Monetary Fund (IMF) will also contribute up to 250bn euros.
Global stock markets surged, with London 5% up at midday, and the euro recovering after last week's tumble.
Hours after the emergency package was announced central banks in Europe reportedly began buying government bonds issued by economies in greatest difficulty.
"The eurozone is certainly regaining confidence," said EU Commission President Jose Manuel Barroso. "Our fundamentals are certainly good."
There had been fears that without the measures, the euro might have come under pressure on markets as investors grew concerned about financially-troubled states such as Portugal and Spain.
The euro strengthened in early trading, surging above $1.30, after hitting a 14-month low against the dollar last week.
At midday in London, the FTSE 100 share index was trading up 255.5 points at 5,314.
This followed a rise in Asian stock markets, with the Japan's Nikkei 225 index up 1.3% and Hong Kong's Hang Seng index climbing 0.8%.
The risk premium on some eurozone government bonds fell sharply, as did the price of insuring them against default.
The rate on two-year Greek bonds fell immediately, from 18.1% to 4.9%.
On Friday, eurozone leaders approved an 110bn-euro loan package to Greece, which will be backed by the EU and IMF.
Speaking early on Monday after 11 hours of talks, Spanish Finance Minister Elena Salgado said an agreement had been reached on a package to defend the euro and eurozone economies.
Under the aid plan, the European Commission would make 60bn euros available to support member states experiencing "difficulties caused by exceptional circumstances beyond their control", she said.
Ms Salgado said eurozone member states would complement such resources through a Special Purpose Vehicle (SPV), known as the European Financial Stabilisation Mechanism and worth 440bn euros, which they would guarantee.
The IMF will contribute an additional sum of at least half of the EU's contribution to the SPV - a total of 250bn euros.
"It shows through this decision that we are placing considerable sums in the interest of stability in Europe," she said.
"Our conclusions also reiterate yet again the need for progress to be made on regulating the financial system, on oversight and the supervision of the financial system, in particular derivatives and the role of rating agencies."
The European Central Bank (ECB) also announced that it would buy eurozone government and private debt "to ensure depth and liquidity in those market segments which are dysfunctional".
EU Monetary Affairs Commissioner Olli Rehn said: "The fiscal efforts of the EU member states, the financial assistance by the commission and by the member states, actions taken today by the ECB prove we shall defend the euro whatever it takes."
Analysts were surprised at the magnitude and co-ordination of the package.
"This truly is overwhelming force, and should be more than sufficient to stabilise markets in the near term, prevent panic and contain the risk of contagion," said Mario Annunziata at UniCredit bank.
The Federal Reserve later said it would re-open currency swap facilities with other major central banks "to help improve liquidity conditions in US dollar funding markets and to prevent the spread of strains to other markets and financial centres".
In an interview with Russian media, US President Barack Obama said: "I am very concerned about what's happening in Europe.
"But I think it is an issue that the Europeans recognise is very serious."