The High Court has ordered the immediate transfer of Anglo Irish Bank's deposit book to AIB.
The deposits of Irish Nationwide Building Society have also been transferred to Irish Life and Permanent.
The direction order was made on the request of the Minster for Finance.
It follows an order made on 8 February, directing the National Treasury Management Agency to organise a tender for the deposit books.
AIB won the tender for the Anglo deposits, believed to be worth just over €9bn, while Irish Life and Permanent was the winning bidder for approximately €4bn of deposits at Irish Nationwide.
Irish Nationwide said that Permanent TSB paid €2.3m for the deposits.
The terms and conditions of the deposits are not affected by the transfer.
Around 500 staff at Anglo and Nationwide will be consulted about transferring with the deposits to the new owners of the books.
Irish Nationwide said that this transfer has no immediate impact for existing mortgage account holders, however the building society no longer accepts new business or top up mortgages for existing customers.
Irish Nationwide's Chief Executive Gerry McGinn has said that
this transfer is an important element of the Government's plans to stabilise the Irish financial system and provides reassurance and protection for depositors.'
The Central Bank of Ireland has said that no action is required by depositors as a result of this transfer.
There will not be any immediate change in how depositors deal with their accounts.
Deposits can be accessed as normal through the relevant institutions and depositors can continue to do business as normal with Anglo Irish Bank and Irish Nationwide.
The Department of Finance has also confirmed depositors both during and after the transfer will be protected under the Credit Institutions Eligible Liabilities Guarantee Scheme 2010 and the Deposit Protection Scheme.
Both institutions will continue to communicate with customers throughout the process.
Any questions regarding individual accounts should be directed to the relevant institution through normal customer contact channels.
Anglo Irish Bank and Irish Nationwide Building Society continue to operate as credit institutions authorised and regulated by the Central Bank of Ireland.
AIB has said that the transfer represents a significant and positive step to improve AIB's liquidity and to reduce its loan deposit ratio.
IBOA General Secretary Larry Broderick has said 'Since the announcement of the sale of these deposits, the IBOA has argued that these should be transferred to Irish institutions and at the same time sought the full protection of staff as part of any transfer.
Irish Life and Permanent TSB senior management has given assurances to staff both in terms of a commitment to no compulsory redundancies and that any redundancies in the future will be on a voluntary basis and protecting the terms and conditions of employment of all staff transferred across.
Mr Broderick said he hopes that a 'meeting takes place between the IBOA and the new Government about a strategic vision for the banking sector which puts people and customers at the centre of these plans rather than focusing simply on propping up financially impaired institutions.'