Greeks queued outside banks as the institutions re-opened on Monday after three weeks of a closure sparked by the deadlock over the country's debt repayment, media reports said.
The withdrawal limit has been increased to up to 420 euros (about $455) a week in one transaction, The Guardian reported.
The initial withdrawal amount was limited to 60 euros ($66) a day, after the shutdown was imposed on June 29 to prevent the financial system from collapsing.
Restrictions on sending money abroad and other controls have not been lifted and the Athens stock market remained closed until further notice.
"Capital controls and restrictions on withdrawals will remain in place but we are entering a new stage which we all hope will be one of normality," Louka Katseli, head of the Greek bank association, said.
According to a report by Greek daily To Vima, the decision to re-open the banks came on Friday afternoon after a teleconference between the Bank of Greece and European Central Bank (ECB). A number of technical issues were resolved in the meeting.
The ministerial decision was issued on Saturday.
People will now be able to deposit cash and transfer cash between existing accounts. They will, however, not be able to open new accounts. An exception to the rule will be made while opening new accounts with regard to the payment of wages, pensions or benefits.
They will be able to issue new debit and credit cards, as well as activate web, mobile and phone banking services.
According to the circular issued by the general secretary of public revenue, a new three-tiered Value Added Tax reform also comes into effect from Monday.
The VAT increase was among a package of reforms demanded by Greece's creditors to open talks on the proposed 86 billion euros ($89 billion) bailout.
The reform sets out three rates -- 6 percent, 13 percent and 23 percent. The low 6 percent rate will apply to medicine, books, newspapers, magazines and theatre tickets.
The 13 percent rate will apply to most fresh meat (pork, lamb, goats, foal, chicken, turkey, rabbits), fish and molluscs (cuttlefish, octopus and squid), milk and dairy products, fresh vegetables, grains, flour, olive oil, bread, pasta and water.
It will also apply to energy, catheters, orthopaedic goods and appliances.
The 23 percent will apply to all other food products, including beef, processed foods, coffee, catering, sweets, salt, hygiene products, computer, school tutoring and language learning services, taxi fares, mass transit tickets, funeral services, and non-exempt medical and dental services.
An architect told BBC that the banks re-opening will make only a small difference to his ability to operate.
"The key challenge is that we cannot pay our suppliers, which means that we will eventually run out of products to sell," Vassilis Masselos said.
