The European Commission has backed the liquidation of Anglo Irish Bank and Irish Nationwide Building Society, which have received €34.7 billion in State aid.
The decision is the first of many legal manoeuvres required to wind down Anglo and the INBS, both of which are now controlled by the State.
They must be formally merged before the years-long liquidation process begins, something which cannot be done without High Court approval.
Although Anglo and the INBS have made tentative plans to proceed with the merger next Friday, Minister for Finance Michael Noonan has yet to approach the court.
Competition commissioner Joaquín Almunia said the state aid chapter on Anglo Irish Bank and INBS had been finally closed.
"I am satisfied that the distortions of competition caused by the enormous aid they have received is satisfactorily addressed by their exit from the market," he said. "Today's decision allows us and the Irish Government to focus on the future of the Irish banking system."
Anglo, which was nationalised in January 2009, has received a total of €29.3 billion from the State after the collapse of its loan book. INBS has received €5.4 billion. The overwhelming bulk of this money will never be recovered.
Neither institution was examined in a sector-wide stress test on the Irish banks in March as they are no longer taking deposits or issuing new loans.
However, a stress test carried out for the Central Bank found last month there was no requirement for any further State aid. The test, by consultants Blackrock Solutions, found previous loan loss forecasts for the INBS remained "robust" while those for Anglo were still "reasonable".
Mr Almunia approved a capital injection of €4.946 billion to Anglo last December, bringing its total State recapitalisation close to €30 billion. At the same time Mr Almunia approved the injection of €2.7 billion to INBS, which brought its total State recapitalisation above €5 billion.
These cash infusions were required to help Anglo and the INBS to meet new capital ratios.
When State support for Allied Irish Banks, the Bank of Ireland and Irish Life Permanent is taken into account, the entire sector is being recapitalised by the taxpayer to the tune of €70 billion.
