The former Anglo Irish Bank is to be liquidated after emergency laws were enacted in Ireland overnight.
The deal following long-running talks with European chiefs aims to ease the burden of the 28 billion euro (£24 billion) bailout of the toxic lender.
After politicians sat through the night to pass legislation with money markets closed, President Michael D Higgins signed it into law.
Finance Minister Michael Noonan was forced to act when reports of an agreement with the European Central Bank (ECB) leaked out on Wednesday afternoon.
The liquidation will be carried out under the Irish Bank Resolution Corporation (IBRC) Bill 2013, the rebranded name for Anglo. The IBRC has assets worth 12 billion euro (£10.3 billion).
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.