Some 126 million coins have been taken out of circulation since a scheme was introduced to round shoppers' bills up or down.
The Central Bank disclosed the extent of its efforts to reduce the use of one and two cents as the first anniversary approaches.
It said a survey showed more than nine out of 10 people think the rounding system is a good idea, or has made no difference to their shopping habits and spending.
The regulator said that almost a year on from the scheme's launch, 80% of retailers around the country are changing bills.
The Central Bank said the one and two cent coins were unique because the cost of minting them was more than their monetary value - 1.65 cent for a one cent and 2.1 cent for a two cent coin.
It said coins were being hoarded or thrown away, and inflation has seen their purchasing power diminish by more than 20%.
John Geelon, deputy head of the Central Bank's payment and securities settlement division, said the amount of coins being handed in was a sign the scheme was being embraced.
"Rounding is conducted on a voluntary basis for both consumers and retailers, so we're pleased to see 80% of retailers are applying it and the vast majority of the public surveyed have no issues with the process," he said.
"Our experience in rounding has been generally positive and we would urge any consumers or retailers who aren't rounding to try the scheme."
Since the euro was introduced in 2001 Ireland has spent €37m issuing one and two cent coins - minting the coppers at three times the rate of the rest of the eurozone.
The rounding scheme was trialled in Wexford in 2013 and businesses and consumers supported the plans.
The Central Bank said both the shopper and retailer have to accept rounding for it to happen and it only applies to cash transactions.