Germany intends to contribute $26.6bn over three years as part of a joint EU-International Monetary Fund (IMF) rescue package of $146bn, spread out over three years.
The bailout has been met with opposition in Germany, with the mass-circulation Bild newspaper criticising what it called the "fattest cheque of all time"
and a poll on Sunday showing 56 per cent of Germans believe handing aid to Athens is wrong.
Many Germans are angry that their tax money is being used to bail out a fellow EU member they feel has been dishonest in its accounting and profligate in its spending, while Germany itself has undergone years of budget-tightening to stimulate its economy.
The deal must also be approved by some other parliaments in eurozone countries - but this is expected to be a formality.
Finance ministers from the 16 euro zoe nations approved the deal on Sunday after Athens adopted a new round of austerity measures that provoked uproar among Greek workers.
Germany, Europe's largest economy and EU founding member, had insisted on the strict austerity package before it would move to free up aid.
But Greece's prime minister has insisted that the new measures are vital for his country's financial survival.
"This is a chance for a fresh start," George Papandreou said.
"We are making changes that should have happened years ago."
The austerity measures include a rise in value-added tax (VAT) to 23 per cent from 21 per cent, a 10 per cent hike in fuel and alcohol taxes and a further reduction in public sector salaries and pensions.
The country's main public sector union ADEDY has vowed to fight the measures, saying they would hit an already weak economy hard.
The ECB, the central bank for the 16 nations that use the euro, said on Monday it was suspending the minimum credit rating requirement for Greece,
to ensure that Greek debt can be used as collateral in ECB lending operations, despite its credit ratings.
"Clearly, desperate times call for desperate actions, and today's ECB decision is one step in the right direction," analysts with the Royal Bank
of Scotland wrote in a research note.