Walsh, who is also the director of the company, said he is leaving the group in order to focus on his “other business interests”.
Compass Group said Walsh will remain as chairman until his successor is appointed, and will not seek re-election at the 2021 AGM. It added that John Bason, senior independent director, will lead the search.
Walsh said: “It has been a privilege to serve for the last six years as chairman of Compass, which is a world-class business and a true British success story on the global stage.
“We have a strong and well-established chief executive in place and I will work to ensure a seamless transition to my successor as chairman.”