Michael Soden admitted he had broken company rules by accessing websites tha were not illegal but contained material of an adult nature.
"This arises from access by me on my PC to internet sites that contain content that infringed the Group's policy on these matters," said Soden in a statement. "I now understand and accept that in doing this I breached the policies of the Bank of Ireland."
The bank decided to make the announcement after the Irisah press was informed of the discovery.
The bank said the resignation was regretful and it would choose his successor soon.
Soden was appointed as head of the bank in 2002.