The governor called it "a day historians will mark as a milestone for equal rights, a day when we did what was right, we did what was just, and we did what was fair."
The law takes effect in June, but opponents are already mounting challenges on several fronts. A group called Preserve Marriage Washington filed Referendum 73. If they collect the more than 120,577 valid voter signatures needed by June 6, the law will be put on hold pending the outcome of a November vote.
Washington is the nation's seventh state to allow same-sex marriage, along with Washington, D.C. The other states are New York, Connecticut, Iowa, Massachusetts, New Hampshire and Vermont.
Meantime, the New Jersey Senate advanced a same-sex marriage bill Monday, and a vote is expected in the New Jersey Assembly on Thursday. But Gov. Chris Christie has vowed to veto the bill if it reaches his desk.
The Associated Press contributed to this report.