Biggest banks in Cyprus will be closed until Thursday (at least) - maybe they will never open?
The agreement protects small savers but depositors with more than 100,000 euros ($130,000; £85,000), many of whom are Russian, face big losses.
Laiki Bank - the country's second largest - will be wound up.
Finance minister Michael Sarris said Cyprus had avoided a "disastrous exit from the eurozone".
President Nicos Anastasiades - who negotiated the deal with the "troika" of the EU, the European Central Bank and the IMF in Brussels - is to address the nation shortly.
Laiki Bank and the Bank of Cyprus - the country's two biggest - will remain closed until Thursday, but all others will reopen on Tuesday after being closed for more than a week, Cyprus's central bank said.