Buck has served as chairman of Chelsea since 2003, when Roman Abramovich bought the Blues.
Chelsea won 21 major trophies in the Abramovich era, including five Premier League titles and two Champions League crowns.
But Abramovich put the club up for sale earlier this year after being sanctioned amid Russia's invasion of Ukraine, with Todd Boehly and Clearlake Capital acquiring the London side.
Buck has subsequently announced he will relinquish his position as chairman and move into a role as senior advisor from 30 June, aiming to help Boehly and his team achieve further success.
"I am proud to have helped Chelsea realise great success on the pitch and make a positive impact in the community," Buck said. "Now is the right time to step down and let new ownership build on the strong foundations we have in place.
"The owners have a compelling vision for Chelsea's future, and I look forward to helping them achieve it in this new role alongside our incredible staff, players, coaches and supporters."
Boehly added: "Bruce has led Chelsea to the highest levels of international and domestic football, while also developing one of the most active social responsibility projects in sport.
"We thank Bruce for his service and his commitment to the club."