Schwarzenegger has expressed an acceptance of gay marriages but said it's an issue that should be decided by voters or the courts, reported the Associated Press.
"He will uphold whatever the court decides," spokesman Margita Thompson said Tuesday after the state Assembly approved the measure, 41-35. The state Senate passed the bill last week.
A state appellate court is considering appeals of a lower court ruling that overturned California laws banning recognition of gay marriages. Opponents of same-sex marriage are trying to get initiatives on the 2006 ballot that would amend the state constitution to ban gay marriages.
Assemblyman Mark Leno, an openly gay San Francisco Democrat, sponsored the bill that passed Tuesday. "Do what we know is in our hearts," he said, the AP reported. "Make sure all California families will have the same protection under the law."
His bill, which would amend state law to define marriage as a civil contract between two people, had failed four times in June, according to Bloomberg News.
"We have embarked upon a slippery slope, and where will that slope stop?" Republican Assemblyman Chuck DeVore said of the vote. "The definition of marriage is between a man and a woman. That's it."
Voters five years ago approved Proposition 22, which prohibits California from recognizing same-sex marriages performed in other states or countries.
California already gives same-sex couples many of the rights and duties of marriage if they register with the state as domestic partners, according to the AP.
Other states have taken action on the issue. Massachusetts' highest court ruled in November 2003 that the state constitution guarantees same-sex couples the right to marry. The nation's first state-sanctioned same-sex weddings began taking place in May 2004.
Vermont began offering civil unions in 2000, after a ruling by the state Supreme Court. And Connecticut earlier this year became the first state to allow civil unions without being forced by the courts, the AP reported.