Buck, an America lawyer who was appointed in 2003 when former owner Roman Abramovich bought the club, will remain as a senior adviser after June 30.
A group led by Todd Boehly and Clearlake Capital acquired Chelsea in May after Abramovich put the club up for sale following Russia's invasion of Ukraine.
"I am proud to have helped Chelsea realize great success on the pitch and make a positive impact in the community," Buck said in a statement.
"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."
The 74-year-old oversaw huge success at Chelsea for both the men's and women's teams. The men's side won two Champions League titles and five Premier League titles, while the women's side have won five domestic trophies in the past two years.
"Bruce has led Chelsea Football Club to the highest levels of international and domestic football, while also developing one of the most active social responsibility projects in sport," Boehly said.
"We thank Bruce for his service and his commitment to the club."