The banking system is almost completely converted to euro, with only a few cash machines in locations such as factories and universities to be put back into service.
The Irish Bankers' Federation said the industry has largely met its targets with bank accounts, point-of-sale machines and Internet and telephone banking systems all converted to the euro.
The Central Bank of Ireland was the only financial institution to open to the public yesterday. According to the bank, up to 3,000 people visited yesterday, with more than 1,500 transactions reported as customers exchanged pounds for euro.
Most customers were typically exchanging amounts of £300, £400 and £500, according to a spokesman. Many of the people who availed of the Central Bank's services indicated they did not hold bank accounts.
An IBF spokesman, Mr Felix O'Regan, pointed out that the service offered by the Central Bank was available to the general public at all banks, building societies and post offices until Irish notes and coins ceased to be legal tender on February 9th.
All financial institutions will exchange up to £500 at a time into euro free of charge for anyone, regardless of whether they have a bank account or not.
Many staff at the Republic's banks and building societies were working behind closed doors to ensure a smooth resumption of business today. Most banks across Europe were also closed.
Mr O'Regan rejected suggestions that the banks should have opened to the public yesterday given the number of people who went to the Central Bank.
The IBF is advising anyone who may have cash saved in their homes to open an account with one of the financial institutions or the post office. Mr O'Regan stressed it could take some time to set up a bank account, and it would be unrealistic for individuals to expect to walk into a financial institution in the run-up to February 9th and expect it to immediately process and lodge large amounts of cash.
Customers are also advised to expect delays and maybe lengthy queues at bank branches when they open today.
While all staff have undergone extensive training, customers are being told to allow more time to transact their usual business as staff and fellow customers get to grips with the new currency. "With a little patience and understanding the transition will be made more smoothly and effectively," the IBF said.
It is estimated that some 80 per cent of the country's ATMs are now dispensing euro. The first reopened from around 6 a.m. with a high number of transactions reported throughout the day.
AIB said 65 per cent of its network was back in service by lunchtime and 85 per cent by close of business. The first customer to withdraw euro from one of its machines yesterday was at its branch in South Mall in Cork at around 8 a.m.
The first retailer to use one of AIB's point-of-sale machines to process sales did so at 4.30 a.m., with garages reporting a high turnover in the early hours.
The State's largest bank estimates that some 33,000 people used its ATMs yesterday to withdraw cash, with a further 54,000 transactions through Laser and credit cards. This is broadly in line with last year's levels, and customers are generally continuing to take out the same amounts of cash as normal.
Bank of Ireland also reported a successful completion of its conversion, with cash machines now largely back in operation. Customers can view a list of the locations which are open at www.bankofireland.ie.
The bank's head of group EMU planning and development, Mr Michael Watson, said it would normally expect to process around 150,000 withdrawals on New Year's Day. By 3 p.m. some 33,000 withdrawals had been made, with customers taking out more than €88 (£70) on average. National Irish Bank and Ulster Bank cash machines were also reopened around the State.