The society was forced to review its management in November 2013 after its former Co-operative Bank chairman Paul Flowers was caught buying and using illegal drugs.
Its chairman Len Wardle resigned as a result of the widely-publicised scandal.
Leighton, who will assume the role immediately, takes over from Ursula Lidbetter who had chaired the group since the review.
‘Vital reform’
The firm’s senior independent non-executive director Sir Christopher Kelly said the “vital reform” and the appointment were highly significant moments for the business.
“We held a thorough and wide-ranging process to appoint our first chair under the new governance framework and Leighton was the outstanding candidate,” he said.
“He has long championed the power of business to benefit local communities and has a reputation for rolling his sleeves up and bringing about sustainable change.”
Richard Pennycook, group ceo of the Co-operative Group, said Leighton had a deep knowledge of the food retail sector.
Leighton was ceo of Asda from 1996 to 2000. Before this he held leadership roles at Royal Mail and Canada’s largest food retailer Loblaw.