The measures, which still have to be adopted by the European Parliament, are aimed at preventing future banking crises and quelling anger over giant public bailouts of lenders by many European countries.
"Our aim is to have a common approach throughout Europe so our taxpayers no longer have to shoulder the burden," said Irish Finance Minister Michael Noonan, who chaired the talks as Ireland holds the EU's rotating presidency.
"The agreement tonight marks a major milestone in our effort to break the vicious link between the banks and the sovereigns," he said, adding that government would no longer have to save banks that were "too big to fail".
The agreement on a key stumbling block towards greater eurozone integration came just ahead of the start of a summit of EU leaders that will aim to tackle another key consequence of the crisis -- youth unemployment.
The crux of the matter was who should foot the bill when a bank fails, and what room for manoeuvre governments can have to decide on a rescue strategy after the widely differing experiences seen in Europe in recent years.
Under the proposed rules, public funds to rescue banks would only be allowed exceptionally after a minimum level of losses equal to eight percent of the total liabilities.
"This establishes 'bail-ins' as the new rule," Noonan said, referring to a term for forced losses.
The Irish presidency said it hoped the new rules would be finalised by early next year at the latest and the plan is that they would then come into effect from 2018.
"This is very important for financial stability in the European Union," French Finance Minister Pierre Moscovici told reporters as he came out of the talks.
His Dutch counterpart Jeroen Dijsselbloem said: "If a bank gets in trouble we will now throughout Europe have one set of rules on who pays the bill."
"The financial sector itself will now to a very very large extent become responsible for dealing with its own problems," he said.
Ministers stressed that bank shareholders and bondholders would be responsible first, followed by depositors with more than 100,000 euros (USD 130,000).
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