The government had been widely expected to take control of Bank of Ireland, the last domestic lender outside of state ownership, after it agreed to underwrite a rights issues, whose results are due on Tuesday.
After the sale and rights issue, the government will own a maximum of 32 per cent in the bank, the finance ministry said.
"The bank is very pleased to see this major endorsement ... and the confidence which these investors share with the bank in the future for the Irish economy," Bank of Ireland said in a statement.
Under the deal the investors will initially purchase €241m worth of the state's shareholding.
They will then purchase the remainder of up to €882m after regulatory approvals. In all they will purchase 4.2bn ordinary shares.
The government said the sale would not involve any additional risk sharing for the government.
Depending on the results of the rights issue, Ireland will end up with between 15 and 32 percent of the bank. Existing shareholders will hold between 31 and 71 per cent and the new investors will hold between 14 percent and 37 percent.
The sale will reduce the size of a state capital injection into the lender required under a IMF/EU bailout deal by 1.1 billion euros to a total of €2.4bn.
The government will thus be able to recapitalise the bank without recourse to EU/IMF funds, the finance ministry said.
Dublin has closed two of its six domestic lenders, merged another two state-controlled institutions and will soon take over a fifth as it seeks to draw a line under a banking crisis that forced the former Celtic Tiger economy into an EU-IMF bailout.