He leaves after six years with the firm citing time pressure on from other business commitments.
He is also a board member of Lloyds Banking Group and has served as deputy chairman since 2009.
Lord Leitch said: “I am sorry to leave but pleased to be continuing my relationship with the Group in an advisory capacity for 2012.”
Sir Win Bischoff, chairman of Lloyds Banking Group, said: “The board and I have accepted with reluctance Sandy Leitch’s wish to retire from the Board after more than six years but respect his commitment to his other roles and the consequent demands on his time.”
Lord Leitch will remain as an adviser to the board for 2012 on insurance and Scottish activities. Glen Moreno will take over his role as deputy chairman.
Lord Leitch is one of two departures for the Group. Tim Tookey, finance director of Lloyds Banking Group is also to leave, at the end of February 2012.
He has worked for the group since 2006 and will be joining insurance firm Friends Life as chief financial officer.
Mr Tookey said: “This has been an important period for the group and I am pleased to have played a part in defining the next stage of the strategy which I fully endorse as the right one to realise the group’s potential.
“With its implementation now underway, this felt like the right time to consider a different challenge.”