Pym had announced in May that he would be stepping down from his current role by the end of the year, and his departure date has now been confirmed as 1 October.
On 13 October, the former Alliance & Leicester boss will join the board as chairman designate of AIB, which was bailed out by the Irish government in 2009.
He said: “I look forward to contributing to the progress that has already been made in re-building a strong bank.
“Irish taxpayers have made considerable sacrifices in supporting the banking system and I am very conscious of my responsibilities in that regard.”
Current AIB chairman David Hodgkinson will retire from the AIB board in December.
Co-op Bank chief executive Niall Booker said the lender, which handed control to its bondholders following the discovery of a £1.5 billion black hole in its finances, has started the search for Pym’s successor. Senior independent director Dennis Holt will act as interim chairman in the meantime.