The bill by Democratic Sen. Alex Padilla, of Los Angeles, would establish safety and performance regulations for autonomous vehicles.
Representatives for Brown say the governor is expected to sign the legislation on Tuesday at the Mountain View headquarters of Google, which has been developing autonomous car technology and lobbying for the California legislation.
Google’s fleet of driverless cars has logged more than 300,000 miles of self-driving on California roads and highways.
Autonomous cars use computers, sensors and GPS technology to operate independently. Backers say they have the potential to make roads safer, pointing out that nearly all car accidents are a result of human error.