Wade, who has led the company for ten years, will be handing over the reins to managing director Simon Champion, and chief operations officer Ben McLaughlin.
He will be staying on with the company as a brand consultant and NED.
Wade sold the majority of his shares to LDC in a management buyout in September 2021, though retains an interest in the company.
He is also the founder of Brands Inc and Boxfresh.
Wade said: “It’s been a great ride over the past 10 years but it’s time to jump off and explore new opportunities. I would like to thank everyone who has helped me on this incredible journey but most of all I would like to thank my wonderful team and family for their support.
“As Rocky Balboa once said ‘Every once in a while a person comes along who defies the odds, who defies logic, and fulfils an incredible dream.”
Boxpark, which was originally founded as a retail-focussed concept, pioneered the use of shipping container boxes for pop-up street food traders.
With sites in Shoreditch, Croydon and Wembley, the group recently agreed a 15-year lease with TfL for the Metropolitan Arcade building, near Liverpool Street station, for an opening in the summer of 2023.
It will open under sister concept BoxHall, an all-day social dining experience, with food, drink and events designed within existing buildings.
The company is also launching a BoxHall site in Bristol, scheduled for summer 2022.