Eurozone nations would grant co-ordinated bilateral loans, totalling some two-thirds of the funding, French President Nicolas Sarkozy said.
The plan was worked out at a summit in Brussels. Greek PM George Papandreou called it "a very satisfactory" move.
The president of the European Council, Herman Van Rompuy, said the deal was significant "not just for Greece, but for the stability of the eurozone".
European Commission President Jose Manuel Barroso said he was "extremely happy that we've reached this deal", calling it "a right decision".
'Last resort'
The joint eurozone and IMF bailout programme envisages strict conditions and requires the unanimous agreement of the 16 eurozone nations to release loans. The agreement included no numbers, but officials in Brussels - speaking on condition of anonymity - said the total package would be some 22bn euros. A draft of the plan, seen by the BBC, says the Greek government "has not requested any financial support", so "no decision has been taken to activate" the mechanism yet.
"We hope that it [the bailout mechanism] will not have to be activated," Mr Van Rompuy said late on Thursday, after the deal was agreed. He added that the deal should tell markets to "have confidence that the eurozone will never abandon Greece". The deal still needs to be backed by the rest of the 27-member EU. The eurozone had avoided seeking an IMF loan for Greece, preferring a European solution and anxious to maintain global confidence in the euro.
Earlier on Thursday Germany's Chancellor Angela Merkel said the German government would "press for emergency aid combining IMF and joint bilateral aid from the eurozone but... only as a last resort".
She has signalled reluctance to offer Greece anything resembling a bail-out, which is not allowed under the single currency rules.
Greece has enacted unpopular measures to curb its deficit, including a freeze on public sector wages, pension reforms and increases in fuel taxes.
It is also having to refinance its debt. Because of doubts over its ability to pay, it is having to pay interest at about 6% - around double what Germany has to pay. Mrs Merkel said she would press for the EU to amend its treaties to strengthen its ability to prevent future budget crises.
Stressing the need to learn lessons from the crisis, she wants a treaty change to allow sanctions to come into force should a eurozone country ever default on its debts. Mr Papandreou urged EU leaders to act to stabilise the euro. The single currency hit a 10-month low against the dollar on Wednesday after a credit downgrade for Portugal, which is also struggling with heavy debts.
Emergency loans
Greece's woes have exposed fundamental disagreements about how the 11-year-old euro project should work, the BBC's Europe business reporter Nigel Cassidy says. The eurozone's governance will have to be re-examined, he adds.
A deal to help Greece could prevent the crisis sapping market confidence in the euro and ease fears of contagion in the eurozone. EU members Hungary, Latvia and Romania have received emergency loans from the IMF and EU as their budgets have been hit hard by the global economic downturn. But, unlike Greece, they are not in the eurozone.
The Greek crisis is not formally on the agenda of the summit, which is officially concerned with the EU's 10-year economic strategy, and reinvigorating international negotiations over global warming. But correspondents say that Greece is on everybody's mind.
German taxpayers are fiercely opposed to bailing out Greece, which is burdened by debt of nearly 300bn euros (£267bn, $407bn) and a public deficit of 12.7% of GDP - more than four times the official eurozone limit.
By: N. Peter Kramer
