Shiv Kumar Yadav has also been charged with "criminal intimidation" of the 26-year-old woman, reports said.
The victim had used the Uber smartphone app to book a taxi home but said she was taken to a secluded area and raped.
Delhi later banned Uber and several other web-based taxi firms for failing to carry out adequate driver checks.
Although the driver has not yet given a statement in public, police say he has confessed to the crime. They say he has also been identified by the victim.
Rape and the issue of sexual violence against Indian women have been in the spotlight in recent years ever since a 23-year-old physiotherapy student was gang-raped and murdered in Delhi in December 2012.
The crime prompted global outrage and a tightening of the laws on sexual violence, but correspondents say they have failed to act as a deterrent.
Earlier this month, five men were arrested in Calcutta for kidnapping and repeatedly raping a Japanese student.
And in the northern Indian state of Uttar Pradesh, two policemen were arrested for allegedly abducting and raping a teenager.
A court in the Indian capital has formally charged a driver of the Uber web-based taxi firm with the rape and kidnapping of a passenger last month.