The measure was one of many approved as lawmakers concluded their session on Thursday, the Los Angeles Times reported.
The driver's license bill is aimed at helping people who have jobs. Young immigrants with temporary federal working papers are already eligible for California licenses.
"This bill will enable millions of people to get to work safely and legally," Brown said in a statement Thursday. "Hopefully, it will send a message to Washington that immigration reform is long past due."
Licenses given to illegal immigrants would be marked DP for driver's privilege rather than DL. It also includes a notice that the license does not establish eligibility for public benefits.
Bills that would allow people in the country illegally to practice law in California and protecting illegal immigrants from fraud also won approval.
The bill on law licenses was inspired by the case of Sergio Garcia, who came to the United States as a child and has been blocked from getting a law license. Federal law would still bar him and others in his situation from practicing law in other states.
The fraud measure is aimed at lawyers and consultants who charge fees for unneeded services. Backers of the bill said they sometimes advertise to offer assistance on changes in federal rules that have not yet become law.