The move follows an application by the Minister for Finance to the court and is the first step in the winding down of the two institutions.
The winding down of the institutions and the transfer of their deposits is required as part of the agreement between the State and the European Union and International Monetary Fund.
The Irish Republic's controversial debt management agency has said it will start an auction process for the sale of the deposits after the Dublin Government submitted restructuring plans for the two state-run lenders to the European Commission last week.
This plan also includes the merger of Anglo Irish and Irish Nationwide.
Anglo Irish said it expected to make a loss of €17.6bn (£14.9bn) in 2010 a figure that would break its own record loss for an Irish company of €12.7bn for the 15 months to December 2009.
NAMA was set up after several Irish banks had to be rescued by the government due to risky lending and the property market crash - but the Dáil Government itself later had to accept a bail-out from the EU and IMF and, under the terms of the €85bn bail-out, had to put forward plans by last week to wind down the loan books and minimise the losses of the two lenders.
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The Irish High Court has now given clearance to those plans.
"The NTMA (National Treasury Management Agency) will immediately commence an auction process to invite interested, fully-licensed financial institutions to tender for Anglo and INBS deposits," the debt management agency said in a statement.
"It is intended that this process will conclude as quickly as possible.
"The process will also involve the amalgamation of Anglo [Irish] and INBS into a merged entity regulated by the Central Bank of Ireland."
The National Treasury Management Agency (NTMA) manages assets and liabilities on behalf of the Irish Government.
It was established at the end of 1990 to borrow for the Exchequer and manage the National Debt.
Since then, its remit has been expanded greatly and now includes the management of the National Pensions Reserve Fund, the National Development Finance Agency, the National Asset Management Agency (NAMA) and the State Claims Agency. Certain banking system functions of the Minister for Finance have also been delegated to the NTMA.
An official statement from NTMA said yesterday: "Depositors will be transferred in a seamless manner and no action is required by depositors. It should be noted that the position of depositors in Anglo and INBS remains fully secure and that any transfer will take place, and be accepted by another credit institution, on the basis of the existing terms and conditions. Depositors will also continue to have full access to their funds both during and after the auction process."
On the banks' staff, the statement continued: "Employees in the business areas of Anglo and INBS that will be affected by the transfer of deposits will be safeguarded in accordance with applicable employment legislation."
(BMcC/GK)
