Hayward, who was BP’s CEO at the time of the Gulf of Mexico disaster, has been chair of the mining and trading group since 2013.
His departure follows the retirement of long-time chief executive Ivan Glasenberg, who was replaced by Gary Nagle at the start of July.
Glencore said Hayward’s departure was agreed with its largest institutional shareholders following a second extension of his tenure as a director beyond nine years.
Kalidas Madhavpeddi will take over as chair. He has been a director at Glencore since February 2020 and has worked in mining for more than 40 years including stints as chief executive of China Moly between 2008 and 2018 and 26 years at Phelps Dodge.
Tony Hayward said: "I am very pleased that the board has appointed Kalidas as my successor.
"His history of working in the resources industry and familiarity of operating across the globe provides excellent experience for this appointment."
Madhavpeddi said: “As the world transitions to cleaner forms of energy and mobility, our portfolio of commodities will allow Glencore to play a key role in helping us achieve the goals of Paris and play a key role in the ongoing energy and mobility transition."
Nagle added: "I look forward to working with Kalidas. His decades of experience across the resources sector will be invaluable to Glencore as we focus on achieving our objectives of sustainable shareholder returns and attaining our ambition of net zero total emissions by 2050 while also focusing on the green energy transition."