Greece has not yet formally requested help from eurozone states
Finance ministers of the 16 eurozone nations have agreed to provide up to 30bn euros (£26bn) in emergency loans for debt-hit Greece it asks for them.
They offered a three-year financing programme at interest rates of around 5%, based on IMF formulas.
Luxembourg Prime Minister Jean-Claude Juncker said there were no elements of subsidy in the loan offer.
Greek Prime Minister George Papandreou said the decision showed that nobody could "play with" the euro.
"With today's decision, Europe sends a clear message: that nobody can play with our common currency, nobody can play with our common fate," he said, speaking on a visit to Cyprus.
"Today, with the Eurogroup decision, the safety net has taken shape. European solidarity has been fleshed out."
Together with at least 10bn euros expected from the IMF in the first year, Greece may receive the biggest multilateral financial rescue ever, Reuters news agency notes.
Mr Juncker said that the eurozone countries had not decided to activate the loans, as this would depend on a decision by the Greek government.
European Commissioner, Olli Rehn: Greece loan 'will be fruitful'
European Commissioner for Economic and Monetary Affairs Olli Rehn said it would be up to the IMF to reveal its precise share of the loan package.
This loan offer means Greece will not have to rely on raising funds in financial markets.
Greece has to find around 11.5bn euros (£10bn) by next month to meet its financial obligations. Its total debt stands at nearly 300bn euros.
An exact interest rate for Greek loans will only be finalised after Greece formally requests help, something it has not previously done.
"The Eurogroup is confident that the determined efforts of the Greek authorities and of its European partners will allow [it] to overcome the fiscal and structural challenges of the Greek economy," said a statement for the eurozone nations.
Although Greece has maintained it does not plan to turn to its eurozone partners and the IMF for any loans, investors believe it will have little choice.
The country has struggled for months to lower its borrowing costs, and the debt crisis has heightened investor fears about rising debt levels and forced down the value of the euro.
Greece intends to auction a 1.2bn euros package of treasury bills on Tuesday.
Last month, the EU and IMF announced plans to provide a 22bn-euro (£20bn; $29.5bn) safety net that could be drawn on should Greece be unable to raise the funds it needs to pay off its debts.
The cost of borrowing on the financial markets for the Greek government has been rising, reaching record levels of 7.5% on Thursday.
Leading ratings agency Fitch had downgraded Greek government debt on Friday.
Fitch downgraded Greece's credit rating by two notches, from BBB+ to BBB-, amid growing fears the country will not be able to resolve its debt problems without help.
The BBB- rating is significant, as this is the lowest rating that qualifies as an investment grade bond. Any further downgrade would mean Greece losing its investment grade status with Fitch.
If the two other major credit rating agencies, Standard & Poor's and Moody's, were to follow Fitch's lead, then a lot of big institutional fund managers, such as pension funds, would not be allowed to invest in Greek debt.
Greece is currently rated BBB+ by Standard & Poor's and A2 by Moody's.
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