Sofia Liu, six, was struck while crossing the road in San Francisco, on New Year's Eve in 2013.
Uber had argued it could not be held responsible for Sofia's death because the driver, Syed Muzzafar, had not had a passenger in his car at the time.
Court documents say the family has asked the court to keep details of the settlement private.
Uber lets people find a car close to their location and catch a ride, like hailing a taxi using a smartphone app.
The company described its drivers as freelancers who were free to log in to the app and accept jobs whenever they pleased.
It said its function was simply to connect a buyer and seller and therefore it was not responsible for what happened between them.
But the family held Uber responsible because the man behind the wheel had been an Uber driver logged into its app at the time of the collision.
Sofia's brother and mother were also struck by the car while the family was crossing the road.
"While nothing will ever bring Sofia back, [the family] is grateful to the American judicial system for providing them a way to resolve the legal issues raised by Sofia's death," the family's lawyer, Christopher Dolan, said.
Uber said: "While we cannot ease their pain, we do hope that this settlement helps the family move forward.
"The Lius suffered a terrible tragedy and our hearts go out to them."
Uber now operates in 57 countries, but has attracted criticism over some of its practices.
In 2013, there were safety concerns after a driver and passenger got into a fight, and it emerged that the driver had had a history of clashes with the law.
More recently, taxi drivers in France have staged protests against the company, with some describing its operations as "illegal".
Lift-sharing company Uber has reached a settlement with the family of a girl who died after she was hit by a car.