The move comes at a time when banks here were expected to cut rates as the European Central Bank will start cutting rates from next week.
Bank of Ireland's move comes just days after fast-growing digital bank Revolut launched a savings product to the Irish market, a move that would raise the stakes for the three main banks.
There is now hope that Revolut has started a price war on savings rates.
Revolut will put pressure on the banks with a new savings product
The money app, which claims to have 2.7 million customers in this country, turned up the pressure, with savings rates reaching 3.49%.
Now Bank of Ireland is set to introduce a new two-year fixed term deposit rate for personal and business customers of 3% APR (annual equivalent rate)
And there will be a new one-year interest rate on deposits with a fixed term for private and business customers of 2.50%.
The new rates will be available from June 6.
The bank said there will be no upward limit on money that can be deposited or on money that will earn interest, while up to 25% of the money can still be withdrawn during the term.
Susan Russell, Bank of Ireland retail director, said: “Our new one and two year fixed term accounts offer better rates, along with flexible features such as accessing some of your cash if needed and easy opening of accounts in a branch or online.
“There is no requirement to open a checking account and no fees or subscriptions to access these rates.”
Daragh Cassidy from price comparison site Bonkers.ie said: “These are competitive rates from Bank of Ireland.
He said that in recent weeks we have seen both N26 and Revolut launch new savings products for their customers in Ireland and this seems to be a clear response to that.”
Mr Cassidy said that although Bank of Ireland's new products have fixed interest rates, customers can withdraw up to 25% of their money over the term, which is not common in the Irish savings market.
He said Irish savers are collectively missing out on billions of euros in interest each year by not putting their money in the best-yielding savings accounts.
Instead, they leave it in accounts that pay little to no interest. And this apathy also helps the banks make record profits.
But with the ECB expected to cut interest rates from next week, now is the time for savers to do something with their money before savings rates also start to fall, Cassidy said.