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”.
Nevada changed its laws to allow self-driven cars in March. The long-term plan is to license members of the public to drive such cars.
Google’s car has been issued with a red licence plate to make it recognisable. The plate features an infinity sign next to the number 001.
Other states, including California, are planning similar changes.
“The vast majority of vehicle accidents are due to human error,” said California state Senator Alex Padilla, when he introduced the legislation.
“Through the use of computers, sensors and other systems, an autonomous vehicle is capable of analysing the driving environment more quickly and operating the vehicle more safely.”