The company has repeatedly argued that its alleged support of Israel has been driven by misinformation online, claiming it has never given money to the Israeli government or military.
The outgoing Mr Narasimhan assumed the role of chief executive at Starbucks in March 2023, having formerly led the consumer goods giant Reckitt, the owner of Durex.
He stepped down from Reckitt mid-way through a three-year turnaround project.
Mr Niccol will start as chief executive at Starbucks on Sept 9, with Rachel Ruggeri, the company’s chief financial officer, serving as interim until then.
Mellody Hobson, Starbucks chairman, said: “Our board believes he will be a transformative leader for our company, our people, and everyone we serve around the world.”