Greece is slated to leave its financial rescue on August 20 and finance ministers from the 19 countries that use the single currency were under pressure to offer Athens a goodbye deal that left it strong in the eyes of the financial markets.
"The Greek crisis ends here tonight," said EU Economic Affairs Commissioner Pierre Moscovici, after marathon talks in Luxembourg.
"We finally got to the end of this path which was so long and difficult it is a historic moment," the former French finance minister said.
The agreement is an important turning point for the eurozone nearly a decade after Greece stunned the world with out-of-control spending and sparked three bailouts and a near collapse of the euro single currency.
The deal was expected to be an easy one, but last-minute resistance by Germany -- Greece's long bailout nemesis and biggest creditor -- dragged the talks on for six hours.
With writing-off loans off the table, eurozone ministers agreed to extend maturities by 10 years on major parts of its total debt obligations, a mountain that has reached 180 percent of GDP -- almost double the country's annual economic output.
The eurozone creditors also agreed to disburse 15 billion euros ($17.5 billion) to ease the country's exit from its programme. This would leave Greece with a hefty 24 billion euro safety cushion, officials said.
"I am happy," Greek Finance Minister Euclid Tsakalotos said after the talks.
But "to make this worthwhile we have to make sure that the Greek people see concrete results... they need to feel the change in their own pockets," he added.