Also next year, Julie Brown will become chief operating and financial officer replacing Fairweather who has decided to pursue new opportunities.
Brown will join from medical technology firm Smith and Nephew.
Burberry chairman Sir John Peace said: "With Julie's appointment, we have an individual who has an outstanding track record in the commercial and financial aspects of a global business as well as business transformation.”
The appointments come two months after the upmarket retailer revealed plans to slash costs by £100 million a year by 2019 as it reported a fall in profits.