Mr Noonan warned that not dealing with the issue could result in potential liabilities of up to 40 billion euro (£34.5 billion) for the country. The liquidation will not affect court cases or legal action taken by the Director of Public Prosecutions, the Government said.
Anglo's former chief executive, Sean FitzPatrick, and two former directors, Pat Whelan and Willie McAteer, are awaiting trial on fraud charges linked to the collapse of the bank.
The contracts of 800-plus employees at the IBRC have been terminated but most workers are expected to transfer to the state's bad bank, the National Assets Management Agency (Nama). Nama will take on all of IBRC's assets and debts.
The liquidation is part of wider proposals being negotiated with the ECB in Frankfurt to revise the costly debt deal used to fund the former Anglo. The money - 31 billion euro (£26 billion) in total when combined with the funds used to cover the collapse of Irish Nationwide Building Society - was paid in using a complex financing mechanism known as promissory notes.
The Government said that it was confident of an agreement with the ECB on rescheduling repayments of the IOUs. A statement from officials in Frankfurt is due this afternoon.