The limits on transactions, which include caps on withdrawals and money leaving the country, are a first in the 14-year history of the euro.
Across Cyprus, large but orderly lines formed ahead of the opening of banks for six hours from noon, and guards from private security firms reinforced police outside some ATMs and banks in the capital, Nicosia. No particular crowd issues were reported.
President Nicos Anastasiades expressed his "warm gratitude and deep appreciation towards the Cypriot people for the maturity and spirit of responsibility they have shown at a critical time for the stability of the Cypriot economy," a statement from his office said.
Banks have been shut in Cyprus since March 16 to prevent people draining their accounts as politicians scrambled to come up with a plan to allow the country to qualify for 10 billion euros ($12.9 billion) in international bailout loans for its stricken financial sector.
A deal was finally reached in Brussels with other euro countries and the International Monetary Fund early Monday. The country's second-largest bank, Laiki, is to be split up, with its healthy assets being absorbed into the Bank of Cyprus. Savers with more 100,000 euros ($129,000) in both Bank of Cyprus and Laiki will face big losses. At Laiki, those could reach as much as 80 percent of amounts above the 100,000 insured limit; those at Bank of Cyprus are expected to be much lower.
The Finance Ministry announced capital controls — to be reviewed daily and initially applying for seven days — to prevent a rush of euros out of the country's banks when they reopened.
They include limiting daily cash withdrawals to 300 euros ($383) per person and limiting payments abroad to 5,000 euros ($6,400). No checks can be cashed, although they can be paid in. Anyone leaving the country, whether Cypriot or a visitor, can only take up to 1,000 euros ($1,290) with them in cash.
The country's general accounting office said pensions and other social security payments, together with salaries for government employees, will be in bank accounts next Tuesday and Wednesday.
Many Cypriots were working out exactly what they could and couldn't do. Television talk shows hosted dial-ins with experts, with viewers' queries ranging from where they would repay loans to how they could pay tuition fees for children studying abroad and handle check payments. Across the country, people wondered whether they would be able to access their salaries, many of which were due this week.
"I believe this will be a very difficult day for both people and bank employees because no matter how much information there was, things were changing all the time," said Costas Kyprianides, a grocery supplier in Nicosia. "Even us traders, like myself, have so many checks which I need to deposit so I can make ends meet."
Some analysts are concerned that, if kept in place long, Cyprus's measures will go against the fundamental principle of the single currency: Free and easy movement of money around the euro's 17 members.
The European Commission said EU member states could restrict financial transactions "in certain circumstances and under strict conditions on grounds of public policy or public security" but added that "the free movement of capital should be reinstated as soon as possible".
Not every account in Laiki and Bank of Cyprus will be hit with big losses. Deposits held by the central government, local authorities such as municipalities, universities and development projects being co-funded by the European Union will not face a so-called haircut. Constantinos Petrides, undersecretary to the president, said the measure was agreed between the Cypriot government and a delegation from the IMF, European Central Bank and European Commission.
Government welfare and pension fund accounts in Laiki will be treated in the same way as those in the Bank of Cyprus, "thereby ensuring most of the deposits," Petrides added.
Some individuals and businesses, spotting that Cyprus's economy was in trouble and that a tax on deposits was being discussed, had moved their money out of Cyprus well before the banks closed their doors last week.
According to ECB figures, deposits in Cyprus' banks slipped 2.2 percent last month, to 46.36 billion euros ($59.36 billion), the lowest figure since May 2010 and down from a peak of 50.5 billion euros ($64.67 billion) in May 2012. The figure excludes deposits from other banks and the central government.
"I anticipated, not this to happen, but I anticipated issues last year, when Greece had a question of whether it will remain in euro and the consequences of that," said Athos Angelides, who runs a business importing and distributing hair salon products. "So luckily we transferred money in the middle of last year over to the UK."
The stock market, which has been closed since March 15, stayed shut. It said it would remain closed also on Friday and Monday, which is Easter in most of Europe. Cyprus follows the Orthodox calendar and does not celebrate Easter until May this year.
Elena Becatoros in Nicosia and David McHugh in Frankfurt contributed.