The Government is to float a quarter of its share in the bailed-out Allied Irish Bank.
Taxpayers poured 21 billion euro into the lender seven years ago in an attempt to pull the economy back from the brink of collapse.
It returned to profitability in 2014.
In a widely expected announcement, Finance Minister Michael Noonan confirmed on Tuesday evening the state will sell 25% of its 99.9% stake.
Mr Noonan said: "The Government's long-held policy is that the state should exit its banking investments in a measured and prudent manner, returning ownership to the private sector over time.
"The strong progress made by AIB and current market conditions mean that now is the right time to commence this process and proceed with an initial sale of approximately 25% of the state's shareholding in AIB, as provided for in the Programme for a Partnership Government."
The shares will be listed on the Irish Stock Exchange and the London Stock Exchange.
The initial public offering (IPO) prospectus and price range are expected to be published in mid-June and it is expected to be one of the largest UK main market IPOs of the last 20 years.
Mr Noonan said the decision is a significant step in the continued normalisation of state involvement in the banking system since the crash.
Bernard Byrne, chief executive of AIB, acknowledged the taxpayers' role in bailing out the lender.
"We acknowledge the very material financial support provided by the state that enabled the bank to undertake this restructure," he said.
"While significant capital has been returned to date, this share listing and sale is very important as it puts in place the final mechanism that will enable the state to continue to recover its investment."