The appointment will be effective immediately and Kane will take charge of office on 29 June 2012.
Kane will also join the board "court of governors", along with new non-executives Prem Watsa, head of Canada’s Fairfax Financial Holdings, and US billionaire Wilbur Ross Jr.
He was appointed to the board of Lloyds in 2000 and remained a member until May 2011, and is also a member of The City UK Supervisory Board, an independent membership body promoting the UK financial services industry.
Kane was shouldering the responsibility for Lloyd’s Scottish Widows insurance arm and banking operations north of the Border.
Bank of Ireland, which is 15.1% owned by the Irish government said that Kane’s exposure in managing a partially state-controlled operation would be beneficial for the firm.
The Irish economy has recently slipped back into recession with rising mortgage arrears.
