The American, who will leave his post at the end of June, will continue to be involved in the club as a senior advisor.
It follows the completion of the Todd Boehly-led consortium’s takeover of Chelsea at the end of May.
“I am proud to have helped Chelsea realise great success on the pitch and make a positive impact in the community,” said Buck. “Now is the right time to step down and let new ownership build on the strong foundations we have in place.”
Buck has been chairman since 2003 after playing a key role in previous owner Roman Abramovich’s acquisition of the club and has overseen huge success on the pitch for both the men’s and women’s teams and major development off it.
Boehly said: “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. We thank Bruce for his service and his commitment to the club.”