Greek banks were remained shut for the last three weeks after financial crisis emerged in the country.
Banks were reopened in Greece and limit on services have been put in place, BBC reported.
Greek people can withdraw 420 euros a week at once instead of just 60 euros a day earlier, but the limit will effectively remain the same and capital controls will also stay in place.
The cautious reopening of the banks, and an increase in value added tax on restaurant food and public transport from Monday, are aimed at restoring trust inside and outside Greece after an aid-for-reforms deal last week averted bankruptcy.
Greece government reached a cash-for-reforms deal aimed at avoiding a debt default and an exit from the eurozone.
Meanwhile, Germany has said it is prepared to consider further debt concessions to Greece.