AIB Group has begun refunding customers who were overcharged on foreign exchange transactions from 1995 until the problem was identified earlier this year.
A spokeswoman for the bank said letters informing affected customers should have arrived in today's post.
The bank lodged money, including interest, into 170,000 accounts on Friday evening.
The bank is to pay out a total of €25.6 million to customers in relation to the foreign exchange overcharging, which was revealed by RTÉ News.
AIB has not identified all those involved, and has asked customers who believe they may have been overcharged to contact the bank.
