The Central Bank has announced a voluntary national rounding scheme to begin on 28 October.
As a result, when customers get change in shops, the amount will be rounded to the nearest 5c, reducing the need for 1c and 2c coins.
The national roll-out follows a successful trial held in Wexford in 2013, where 85% of consumers and 100% of retailers wanted the policy introduced nationally.
Under the scheme, rounding will be conducted on a voluntary basis and will only be applicable to cash payments.
One and two cent coins will remain legal tender, with the total amount of any bill rounded up or down to the nearest five cent.
In a statement, the Central Bank said consumers will be entitled to opt out of rounding and may ask for their exact change.
Speaking on RTÉ's Morning Ireland, Ronnie O'Toole of the Central Bank said, from the bank's experience, consumers do not like one and two cent coins.
"What we saw is that we were producing them in huge numbers. Retailers were giving them to consumers; consumers were putting them in jam jars. Retailers were coming back to us and saying we need new one and two cent coins," Mr O'Toole said.
"We have produced around 2.5 billion [one and two cent coins] since the launch of the euro, that's 1,500 for every household, but there are very few in circulation because people are not putting them back.
"People prefer not using them to actually using them and they have these stockpiled at home."
Mr O'Toole said the cost of producing a one cent coin is actually around 1.7 cent, meaning they lose value as soon as they are minted.
He also said prices will not change, but change will be rounded to the nearest 5c.
"If the total bill is €11.21 it will round down to €11.20, if it is €11.24 it rounds up to €11.25. Half the time you will gain one or two cents, half the time you will lose one or two cents.
"It will balance out very quickly for the consumer and the retailer, the only difference will be that we won’t be carrying around a big pocket of brown coins."
Meanwhile, a number of charities are encouraging people to donate their hoarded coinage to good causes.