McGeorge stepped down after returning to New Look as executive chairman in November 2017 to “begin the Company’s turnaround strategy”.
Coupe previously worked at J Sainsbury plc as CEO, and is also non-executive chairman of Oak Furnitureland and Harding Retail.
McGeorge said: “After four years as chairman, now is the right time for me to stand down. New Look is in a remarkably better position now than it was when I returned to it in 2017.
“I leave the business in incredibly capable hands and the company will benefit greatly from Mike’s invaluable expertise, experience and oversight as it looks to continue on the positive trajectory it is set on.”
Coupe said: “I am delighted to be joining New Look at this moment in time. As a leading womenswear brand known for its broad appeal fashion, the business has a significant opportunity to capitalise on through its omnichannel model and loyal customer base.
“I am looking forward to working closely with Nigel and the rest of his team to deliver long-term and sustainable growth.”
Nigel Oddy, chief executive officer, added: “Alistair’s contribution to New Look has been invaluable. He has provided strategic vision, operational experience, and wise counsel to the board during his tenure.
“I am delighted that Mike is joining the company as chairman, and having spent time with him already, we both share the same excitement and enthusiasm to deliver on our strategy..”