Kalanick, who helped found the company in 2009, is reported to have quit following shareholder unrest over his leadership.
Uber has been dogged by questions over its working culture, including sexual harassment, allegations of trade secrets theft and an investigation into efforts to mislead government regulators.
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Heavyweight investors – Benchmark, First Round Capital, Lowercase Capital, Menlo Ventures and Fidelity Investments wrote a letter titled “Moving Uber Forward”, demanding Kalanick steps down, according to The New York Times.
As well as Kalanick’s immediate resignation, they demanded the board appoints more “truly independent directors” and that Uber hires an experienced finance chief.
Kalanick said: “I love Uber more than anything in the world and at this difficult moment in my personal life I have accepted the investors’ request to step aside so that Uber can go back to building rather than be distracted with another fight.”
He had already been on indefinite leave amid criticism of his management style and following the death of his mother in a boating accident.
An Uber spokesman said: “Travis has always put Uber first. This is a bold decision and a sign of his devotion and love for Uber.
“By stepping away, he’s taking the time to heal from his personal tragedy while giving the company room to fully embrace this new chapter in Uber’s history. We look forward to continuing to serve with him on the board.”
Uber has embarked on a 180-day programme to change its image by allowing riders to give drivers tips through the Uber app, something the company had resisted under Kalanick.
The Silicon Valley company is valued at more than $60 billion (£47bn).