The state Assembly approved the same-sex marriage measure, 41-35, on Tuesday. The Senate had approved it last week.
Schwarzenegger previously expressed an acceptance of same-sex marriages but said it is an issue that should be decided by voters or the courts.
Five years ago, Californians overwhelmingly passed Proposition 22, the Defense of Marriage Act, to protect traditional marriage.
Tony Perkins, president of the Washington, D.C.-based Family Research Council, said in a statement: «A legislature that does not heed the will of the people is not a legislature that is functioning as it is meant to function.» His group urged the governor to veto the measure.
