Kalanick had already been on a leave of absence aimed at restoring confidence in the scandal-plagued ridesharing giant.
The New York Times reported earlier Wednesday that five of the company's major investors had demanded his departure.
"I can confirm Travis has resigned," the spokesman told AFP in an email.
He also quoted from a board statement saying that "Travis has always put Uber first".
"This is a bold decision and a sign of his devotion and love for Uber," the board said.
The pioneering company has been facing pressure to rein in a no-holds-barred management style led by Kalanick and to reform its workplace culture, which has sparked charges of harassment and discrimination.
Kalanick is to stay on as a board member, Uber said.
The investors, who made their demand in a letter, include one of Uber's biggest shareholders, the venture capital firm Benchmark, the New York Times said.
In the letter, titled "Moving Uber Forward", the investors told Kalanick that he must immediately leave and that the company needed a change in leadership, the Times reported.
Kalanick consulted with at least one Uber board member and after long discussions with some of the investors, he agreed to step down, the paper 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," Kalanick said in a statement, quoted by the Times and confirmed by Uber.
Last week, Kalanick said one of the reasons for taking a leave of absence was the recent death of his mother.
Uber, which is the world's richest venture-backed startup valued at some $68 billion, operates in dozens of countries despite problems with regulators in many jurisdictions and protests from established taxi operators.
Kalanick had been seen as the driving force behind Uber despite a series of embarrassing missteps.
