The California State Assembly unanimously voted Thursday to approve the name change. The bill now heads to the U.S. Senate.
More than 61,000 fans have signed a Change.org petition to name the tunnel for Williams.
The tunnel, which has a rainbow painted on the outside, is currently named after William Waldo, a Whig Party candidate who ran for governor in 1853.
Williams committed suicide in August. He grew up and lived in Marin County.
The Associated Press contributed to this report