Mr Fingleton had intended to retire on 28 February but deferred his retirement to the end of this month following Michael Walsh's resignation as chairman in February.
The move follows pressure from the Government on Irish Nationwide to change the structure of the building society's board and how it operates at executive level.
Daniel Kitchen, who is currently a director, will become non-executive chairman of the society, having turned down the position of chief executive because of the Government's proposal to cap top bankers' pay.
But, a statement from Irish Nationwide says that while the search for a new chief executive goes on Mr Kitchen will assume this position of chief executive in the short term.
The board hopes to amend the rules at its next annual general meeting to increase the number of directors from eight to ten.
