Norman, a former Conservative MP, will join M&S as non-executive chairman on 1 September and succeed Robert Swannell, who is retiring.
Norman said: "I am looking forward to taking on the role of the chairmanship of Marks & Spencer as the business under Steve Rowe’s leadership faces into the considerable challenges ahead in a rapidly changing retail landscape."
Norman was replaced by Sir Peter Bazalgette as ITV chairman last year after six years in the role. He made his name as the man who, along with Allan Leighton, turned Asda around after joining the struggling retailer in 1991, transforming it into the second largest supermarket group in the UK before it was acquired by Wal-Mart in 1999.
Norman also had an eight-year stint as a Conservative MP for Tunbridge Wells before standing down at the General Election in 2005.
He then acquired the telecoms firm Energis, working to improve its fortunes over a three-year period before selling it to Cable & Wireless.
Norman has also served in chairman roles at Lazard London and Hobbycraft.
The appointment comes a day after M&S unveiled its first brand campaign created by Grey London since switching ad agencies last summer. The "Spend it well" campaign aims to position M&S as an enabler of a life well-lived.
In a busy week for the retailer, it has also hired Halfords chief executive Jill McDonald to turn around its non-food business, with responsibilities taken from M&S boss Steve Rowe.
Last month M&S said it would open 36 new stores in the UK over the next six months, as well as starting a food home-delivery service.
Vindi Banga, senior independent director at M&S, led the selection process. He said: "Archie is one of the most respected business leaders in the UK with extensive experience as both CEO and chair, and a proven record in retail and other areas."