The rescue package is intended as a back-up plan in case Greece is no longer able to raise funds to repay its debts and finance its budget on financial markets because of excessively high interest rates.
Greece’s debts were last tallied at some 300 billion euros.
The decision to spell out the scale and the terms of the aid, which will involve all of the euro zone members, was aimed at soothing markets that have dragged down the euro against the dollar and forced up the interest rates Greece has to pay to borrow money.
George Papandreou, Greece's prime minister, said in a statement: "With today's decision, Europe sends a very clear message that no one, any longer, can play with our common currency, no one can play with our common fate."
In a rare weekend telephone conference, finance ministers of the 16 nations that share the single European currency backed a detailed plan for Greece to borrow from euro-zone governments and the IMF at significantly below market rates.
Dominique Strauss-Kahn, the IMF chief, said the fund was ready to provide help, possibly through a multi-year standby loan arrangement.
He added that the IMF was set to hold talks with Greek, EU and European Central Bank officials in Brussels on Monday.
"The IMF stands ready to join the effort, including through a multi-year stand-by arrangement, to the extent needed and requested by the Greek authorities," Strauss-Kahn said in a statement.
He welcomed the euro zone's financial package for Greece, calling it an important step that will also help safeguard financial stability in the euro area as a whole.
If Greece obtains the money, the package could dwarf past IMF bailouts for Mexico and Argentina.
The largest IMF commitment ever made to a country was the $47bn arrangement for Mexico approved in April 2009 under a so-called flexible credit line.
Mexico has not drawn from the credit line.
The firepower in the Greek package, even if held in reserve, may reassure investors and make them more willing to continue buying Greek bonds.
But big uncertainties remain over the longer-term prospects for reducing Greece's debt mountain, which have dented confidence in the euro.