Mr Norman, who built his reputation as boss of Asda, will replace Robert Swannell, who joined M&S in 2010, the BBC reports.
The announcement comes days after M&S hired the boss of Halfords, Jill McDonald, to take charge of its clothing, home and beauty business.
Mr Norman, former executive at retailer Kingfisher, stood down as ITV chairman last year.
In a statement, Mr Swannell said: “I am delighted that Archie, with his deep, relevant experience is to be M&S’s next chairman.
“It has been a real privilege to have served as chairman and to have worked with so many exceptional people who are so passionate about this great business.
“With the appointment of Steve Rowe in 2016, I am confident that we have an excellent team, well-equipped to grow and strengthen the business. I wish them all the very best for the future.”
Mr Norman has a reputation for turning around businesses.
He is most famously credited with transforming Asda, which was ailing at the beginning of the 1990s but was sold for £6.5bn to Wal-Mart in 1999.
He admitted that it meant tough decisions such as thousands of redundancies, and salary freezes.
Mr 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.”
Mr Norman joins M&S as chief executive Steve Rowe continues the fight to improve flagging clothing sales, and revamp product ranges and prices, while attempting to create a leaner and more focused business.
M&S shares rose more than 2 per cent in morning trading to 364.80p.