NIB staff have had voted to accept the transition programme on work practices and training negotiated by the IBOA and NIB's new owners, Danske Bank.
The proposed "enabling agreement" rules out the prospect of compulsory redundancies and offers staff a range of incentives to undertake new training courses.
Larry Broderick of the IBOA said the vote signals "an important vote of confidence by staff in Danske Bank and their future plans and investment programme for National Irish Bank."
Danske Bank, which has also acquired Northern Bank, plans to merge the two banks and has asked staff to complete a computer training course to help with the integration process.
To compensate staff Danske Bank has offered each staff member a home computer worth €2,160 at no cost to them. They will also receive a one year free subscription to broadband.
Mr Broderick said the IBOA will also be clarifying with senior management in the coming days, details around training and working arrangements and overtime for staff in the lead up to the change in ownership.