The glitch saw large queues form at some cash machines on Tuesday and into the night, as word spread on social media, prompting police to be called in.
Some reports said customers with no money in their accounts were able to withdraw up to 1,000 euros ($1,100).
The bank warned customers that withdrawals and transfers, including those over normal limits, would be debited from accounts, potentially tipping them into costly overdrafts.
Announcing the fix, it added: "Overnight payments to accounts may appear throughout the day. We sincerely apologise for the disruption this outage caused.
"We know it fell far below the standards our customers expect from us."
Brendan Burgess, founder of the website AskAboutMoney.com, told broadcaster RTE the bank needed to improve its "clunky" IT systems.
But he added: "If you withdrew 1,000 euros... then queued up outside the ATM machine to withdraw that money I don't think you deserve any leeway at all.
"Fraud is fraud. If you know you have no money and you take 1,000 euros out of a bank account and you know it's not there that's fraud. Let's not say this is a problem with Bank of Ireland systems."
The Central Bank of Ireland previously fined Bank of Ireland for deficiencies in its IT systems, and said it was monitoring the implications of the outage.
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