The Delhi court found Shiv Kumar Yadav guilty of raping the 25-year-old woman as she returned home from dinner with friends in the Indian capital.
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"He has been convicted and found to be guilty for all charges against him, which include rape," public prosecutor Atul Shrivastava told AFP after the verdict was delivered.
He will be sentenced on October 23 after being convicted on four charges - rape, abduction, intimidation and causing harm.
"(The) court has convicted him for all the sections for which he was charged," defence lawyer Dharmender Kumar Mishra told reporters outside the court.
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Uber was banned from operating in Delhi in the aftermath of the December 5 attack.
Yadav was tried by one of the special fast-track courts introduced in 2013 following the fatal gang-rape of a student on a bus in Delhi, a crime that shocked the nation and sparked angry protests about India's treatment of women.
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Uber was accused of failing to conduct adequate background checks after it emerged that Yadav had been accused of assaulting other women, although he had no previous convictions.
The California-based startup's rapid international growth has sparked tensions with rival taxi companies, which protest that Uber cars are not subject to the same regulations.
Uber set up its India operation in September 2013, and now operates in around a dozen Indian cities.
It resumed operations in New Delhi earlier this year.
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