Euan Sutherland will become group chief executive in May, replacing Peter Marks, who is retiring.
Mr Sutherland, 43, is currently group chief operating officer at Kingfisher.
He was previously chairman of B&Q and chief executive of Kingfisher in the UK & Ireland.
Mr Sutherland said: “The Co-operative is a great brand and I am very pleased to be given the opportunity to lead the organisation at this important time.
“The challenge is to build upon the success that has been achieved in recent years and the solid foundations that have been laid for its future growth.”
Len Wardle, chairman of The Co-operative Group, said: “He brings with him considerable experience of the strategic leadership needed in complex customer-facing businesses, across a variety of retail sectors, and we very much look forward to welcoming him and working together.”