The bill will establish safety and performance regulations to test and operate autonomous vehicles on state roads and highways.
"Today we're looking at science fiction becoming tomorrow's reality -- the self-driving car," Brown said.
Google has been developing autonomous car technology and lobbying for the regulations. The company's fleet of a dozen computer-controlled vehicles -- mostly Priuses equipped with self-driving technology -- has logged more than 300,000 miles of self-driving without an accident, according to Google.
"I think the self-driving car can really dramatically improve the quality of life for everyone," Google co-founder Sergei Brin said.
The Alliance of Automobile Manufacturers expressed concern that California is moving too quickly to embrace self-driving cars.
"Currently, autos are designed to be operated by people who carry the responsibility to maintain control and safely operate the vehicle," the trade group said in a statement. "Unfortunately this legislation lacks any provision protecting an automaker whose car is converted to an autonomous operation vehicle without the consent or even knowledge of that auto manufacturer."
Autonomous cars, which could be sold commercially within the next decade, use computers, sensors and other technology to operate independently, but a human driver can override the autopilot function and take control of the vehicle at any time.
With smartphone-wielding drivers more distracted than ever, backers say robotic vehicles have the potential to make roads significantly safer, noting that nearly all car accidents are a result of human error.
The legislation requires the California Department of Motor Vehicles to draft regulations for autonomous vehicles by Jan. 1, 2015. Currently, state law doesn't mention self-driving cars because the technology is so new.
The regulations would allow vehicles to operate autonomously, but a licensed driver would still need to sit behind the wheel to serve as a backup operator in case of emergency.
The legislation is also aimed at keeping California at the forefront of the autonomous car industry since Stanford University and Silicon Valley companies have been working on the technology for years.
In February, Nevada became the first U.S. state to approve regulations spelling out requirements for companies to test driverless cars on that state's roads.
Carmakers such as Audi AG, BMW AG, Ford Motor Co. and Volvo have been working on autonomous car technology for years.
In recent years, automakers also have been introducing autonomous functions such as self-parking, lane departure warnings and adaptive cruise-control, which allows vehicles to automatically accelerate and decelerate with the flow of traffic.
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