Mr Norman will succeed Robert Swannell, who is retiring after six years in the role, when he takes up the position on September 1.
Best known for turning Asda around in the 1990s, he has also served as chairman of ITV, Lazard and Hobbycraft, as well as stints at Kingfisher and Energis.
Mr Norman joins M&S as chief executive Steve Rowe continues the fight to improve under-pressure sales in its clothing arm, overseeing a wide-ranging overhaul which will see it shut stores and revamp its product ranges and prices.
He 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."
The announcement comes days after M&S revealed it has poached the chief executive of Halfords and put her in charge of shoring up its embattled clothing arm.
The high street bellwether said on Wednesday that Jill McDonald had been recruited into the new role of managing director for clothing, home and beauty, joining the retailer this autumn.