The first to hit the highway will be a Toyota Prius modified by search firm Google, which is leading the way in driverless car technology.
Its first drive included a spin down Las Vegas's famous strip.
Other car companies are also seeking self-driven car licences in Nevada.
The car uses video cameras mounted on the roof, radar sensors and a laser range finder to "see" other traffic.
Engineers at Google have previously tested the car on the streets of California, including crossing San Francisco's Golden Gate bridge.
For those tests, the car remained manned at all times by a trained driver ready to take control if the software failed.
According to software engineer Sebastian Thrun, the car has covered 140,000 miles with no accidents, other than a bump at traffic lights from a car behind.
Bruce Breslow, director of Nevada's Department of Motor Vehicles, says he believes driverless vehicles are the "cars of the future".