The proposal from Democratic Assemblyman Steven Bradford of Gardena is intended to better protect cyclists from aggressive drivers. It states that if drivers cannot leave three feet of space, they must slow down and pass only when it would not endanger the cyclist's safety.
Bradford's bill was sponsored by Los Angeles Mayor Antonio Villaraigosa, an avid cyclist who was injured in 2010 after a taxi driver abruptly pulled in front of him.
Brown announced signing AB1371 on Monday. He vetoed legislation last year that would have allowed drivers to cross a double-yellow line to make room for a cyclist.
The law will go into effect on Sept. 16, 2014.