Taoiseach Enda Kenny said expensive IOUs written to fund the collapsed lender will be replaced with bonds running for 34 years on average.
It is hoped the arrangement, signed off by ECB chiefs at their meeting in Frankfurt over the past 24 hours, will save the country billions.
"Today's outcome is a historic step on the road to economic recovery," Mr Kenny told the Irish Parliament.
"The agreement has reduced Ireland's vulnerability from the huge debts taken on by Irish taxpayers as a result of the cost of rescuing failed private banks."
Irish citizens can look forward once again with positive expectations
Taoiseach Enda Kenny
The new deal will cancel out a debt repayment instalment of €3.1bn due in March and every subsequent March in the next decade.
The Republic's annual interest rate will now be set at 3%.
The plan was negotiated in conjunction with the Irish government liquidating the former Anglo Irish under emergency laws, after politicians debated overnight on Wednesday.
ECB president Mario Draghi said members of the bank backed the rescheduling of debt.
He continued: "The governing council unanimously took note of the Irish operation".
Anglo Irish, now known as the Irish Bank Resolution Corporation (IRBC), has assets worth €12bn.
However, it was dissolved following talks with European chiefs as part of action to ease the burden of the IRBC €28bn bailout.
President Michael D Higgins signed the liquidation order after money markets closed. It is thought the Irish Finance Minister's hand was forced after reports of an agreement with the European Central Bank leaked on Wednesday afternoon.
More than 800 people were employed at the IRBC, but most are expected to transfer to the state's bad bank, the National Assets Management Agency (Nama).
A total of €31bn was used to cover the collapse of Irish Nationwide Building Society, whose assets were transferred to Anglo. The money was paid using a complex finance mechanism known as promissory notes.
Sinn Féin president Gerry Adams warned that when the deal is done the original debt may now be larger, due to interest.
"Sinn Féin does not accept that restructuring or repaying these debts over a longer time frame is a credible deal for the taxpayer," he added.