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The agreement emerged after fraught negotiations between President Nicos Anastasiades and heads of the European Union, the European Central Bank and the International Monetary Fund - hours before a deadline to avert a collapse of the banking system.
The plan, swiftly endorsed by euro zone finance ministers, will spare the east Mediterranean island a financial meltdown by winding down Popular Bank of Cyprus
Deposits above 1,00,000 euros, which under EU law are not guaranteed, will be frozen and used to resolve debts, and Laiki will effectively be shuttered, with thousands of job losses.
An EU spokesman said no levy would be imposed on any deposits in Cypriot banks. A first attempt at a deal last week collapsed when the Cypriot parliament rejected a proposed levy on all deposits.
A senior source involved in the talks said Anastasiades had threatened to resign at one stage if he was pushed too far.
EU diplomats said the President, flown to Brussels in a private jet chartered by the European Commission, had fought to preserve the country's business model as an offshore financial centre drawing huge sums from wealthy Russians and Britons.
The key issues in dispute were how Cyprus would raise 5.8 billion euros from its banking sector towards its own financial rescue, and how to restructure and resolve the outsized banks.
The EU's economic affairs chief Olli Rehn said there were no good options but "only hard choices left" for the latest casualty of the euro zone crisis.
With banks closed for the last week, the Central Bank of Cyprus imposed a 100-euros per day limit on withdrawals from cash machines at the two biggest banks to avert a run.
French Finance Minister Pierre Moscovici rejected charges that the EU had brought Cypriots to their knees, saying it was the island's offshore business model that had failed.
"To all those who say that we are strangling an entire people ... Cyprus is a casino economy that was on the brink of bankruptcy," he told Canal Plus television.
The euro gained against the dollar on the news in early Asian trading.
Analysts had said failure to clinch a deal could cause a financial market selloff, but some said the island's small size - it accounts for just 0.2% of the euro zone's economic output - meant contagion would be limited.
The abandoned levy on bank deposits had unsettled investors since it represented an unprecedented step in Europe's handling of a debt crisis that has spread from Greece, to Ireland, Portugal, Spain and Italy.
Anxious Mood
In the Cypriot capital, Nicosia, on Sunday the mood was anxious.
"I haven't felt so uncertain about the future since I was 13 and Cyprus was invaded," said Dora Giorgali, 53, a nursery teacher who lost her job two years ago when the school she worked at closed down.
"I have two children studying abroad and I tell them not to return to Cyprus. Imagine a mother saying that," she said in a central Nicosia square. "I think a solution will be found tonight but it won't be in the best interests of our country."
Cyprus's banking sector, with assets eight times the size of its economy, has been crippled by exposure to Greece, where private bondholders suffered a 75% "haircut" last year.
Without a deal by the end of Monday, the ECB said it would cut off emergency funds to the banks, spelling certain collapse and potentially pushing the country out of the euro.
Conservative leader Anastasiades, barely a month in office and wrestling with Cyprus' worst crisis since a 1974 invasion by Turkish forces split the island in two, was forced to back down on his efforts to shield big account holders.
Anticipating a run when banks reopen on Tuesday, Parliament has given the government powers to impose capital controls.
ParliamentAbout 200 bank employees protested outside the presidential palace on Sunday chanting "troika out of Cyprus" and "Cyprus will not become a protectorate".
In a stunning vote on Tuesday, the 56-seat parliament rejected a levy on depositors, big and small. Finance Minister Michael Sarris then spent three fruitless days in Moscow trying to win help from Russia, whose citizens and companies have billions of euros at stake in Cypriot banks.
On Friday, lawmakers voted to nationalise pension funds and split failing lenders into good and bad banks - the measure likely to be applied to Laiki. The plan to tap pension funds was shelved due to German opposition, a Cypriot official said.
The revised bailout plan many not require further parliamentary approval since the idea of a levy was dropped.
The tottering banks hold 68 billion euros in deposits, including 38 billion in accounts of more than 1,00,000 euros - enormous sums for an island of 1.1 million people which could never sustain such a big financial system on its own.
