The deal includes an agreement for Cyprus to raise taxes, cut its deficit and reduce its dependence on the banking sector, the BBC reported Saturday.
"The Euro Group was able to reach a political agreement with the Cypriot authorities on the cornerstones of this agreement," said Jeroen Dijsselbloem, the head of the Euro Group. "The assistance is warranted to safeguard financial stability in Cyprus and the eurozone as a whole."
"We don't want a Band-Aid. We want something that lasts, that is durable and sustainable," said International Monetary Fund Director Christine Lagarde, who participated in negotiations on the bailout.
Bank depositors are expected to contribute $7.5 billion to the package through a one-time 6.75 percent tax levied on bank accounts of less than $130,800 and a 9.9 percent tax on accounts worth more than that.
The taxes are already being collected to safeguard against massive withdrawals of funds from the country, officials said.
The Qatari-owned news network al-Jazeera reported Saturday people lined up at ATMs to try to get their money out of banks.
Government spokesman Christos Stylianides said the situation was "is serious but not tragic, there is no reason to panic."
He said the government had to choose "between saving the economy and a disorderly default."
"There is a general political sentiment that it is not acceptable to be bailing out a country, and thereby putting European taxpayers' money at risk, to basically protect Russian depositors in Cypriot banks," said economist Jacob Funk Kirkegaard at the Peterson Institute for International Economics.
There has been speculation Russia could help finance the bailout by granting a $2.5 billion loan to Cyprus. Cypriot Finance Minister Michael Sarris is scheduled to visit Moscow Monday, the BBC said.