The action comes a day after a federal appeals court declared California's ban on gay marriage unconstitutional, saying it was a violation of the civil rights of gay and lesbian couples.
The Washington House passed the bill on a 55-43 vote. The state Senate approved the measure last week. And Democratic Gov. Chris Gregoire is expected to sign the measure into law next week.
Democratic Rep. Jamie Pedersen, a gay lawmaker from Seattle who has sponsored gay rights bills in the House for several years, said that while he and his partner are grateful for the rights that exist under the state's current domestic partnership law, "domestic partnership is a pale and inadequate substitute for marriage."
Pedersen cited Tuesday's ruling by the San Francisco-based 9th U.S. Circuit Court of Appeals during his remarks on the House floor.
"The court addressed the question of why marriage matters directly," he said, and read a section from the ruling that stated "marriage is the name that society gives to the relationship that matters most between two adults."
"I would like for our four children to grow up understanding that their daddy and their poppa have made that kind of a lifelong commitment to each other," he said. "Marriage is the word that we use in our society to convey that idea."
Several Republicans argued against the bill, saying that it goes against the tradition of marriage.
Rep. Jay Rodne, R-Snoqualmie, said that the measure "severs the cultural, historical and legal underpinnings of the institution of marriage."
"This bill is really an exercise of raw political power," he said. "It contravenes human nature and it will hurt families and children."
Two Republicans crossed the aisle and voted in favor of the bill. Three Democrats voted against it. Democrats hold a 56-42 majority in the House.
Rep. Maureen Walsh, R-College Place, said that the bill was a matter of equality.
"Why in the world would we not allow those equal rights to those individuals who are truly committed to each other in life?" she asked. She noted that her daughter told her she was gay a few years ago.
"Nothing's different," she said. "She's still a fabulous human being. And some day, by God, I want to throw a wedding for that kid."
Gregoire watched from the wings with the bill's sponsor, Democratic Sen. Ed Murray of Seattle, a gay lawmaker who has spearheaded the domestic partnership and marriage push in the Legislature.
"I'm happy," Murray said after the vote. "It's a great day for families across the state. It's a great day for my family."
However, gay couples can't begin walking down the aisle just yet.
The proposal would take effect 90 days after the governor signs the measure but opponents have promised to fight gay marriage with a ballot measure that would allow voters to overturn the legislative approval.
If opponents gather enough signatures to take their fight to the ballot box, the law would be put on hold pending the outcome of a November election.
Otherwise gay couples could wed starting in June.
Washington state has had domestic partnership laws since 2007, and more than a dozen other states have provisions, ranging from civil unions to gay marriage, supporting same-sex couples.
Gay marriage is legal in New York, Connecticut, Iowa, Massachusetts, New Hampshire, Vermont and Washington D.C.
Lawmakers in New Jersey are expected to vote on gay marriage next week, and Maine could see a gay marriage proposal on the November ballot.
Proposed amendments to ban gay marriage will be on the ballots in North Carolina in May and in Minnesota in November.
A three-judge panel of the 9th Circuit ruled against California's voter-approved same-sex marriage ban, known as Proposition 8.
The panel gave gay marriage opponents time to appeal the 2-1 decision before ordering the state to allow same-sex weddings to resume. The judges also said the decision only applies to California, even though the court has jurisdiction in nine western states.
Lawyers for the coalition of conservative religious groups that sponsored Proposition 8 said they have not decided if they will seek a new 9th Circuit hearing or file an appeal directly to the U.S. Supreme Court.
Washington state's momentum for same-sex marriage has been building and the debate has changed significantly since 1998, when lawmakers passed Washington's Defense of Marriage Act banning gay marriage. The constitutionality of that law ultimately was upheld by the state Supreme Court in 2006. But earlier that year, a gay civil rights measure passed after nearly 30 years of failure, signaling a change in the Legislature.
The quick progression of domestic partnership laws in the state came soon after, with a domestic partnership law in 2007, and two years of expansion that culminated in 2009 with "everything but marriage" expansion that was upheld by voters.
In October, a University of Washington poll found that an increasing number of people in the state support same-sex marriage. About 43 percent of respondents said they support gay marriage, up from 30 percent in the same poll five years earlier. Another 22 percent said they support giving identical rights to gay couples, without calling the unions "marriage."
If a challenge to gay marriage law was on the ballot, 55 percent said they would vote to uphold the law. And 38 percent said they would vote to reject a gay marriage law.
The gay marriage bill also has the backing of several prominent Pacific Northwest businesses, including Microsoft, Nike and Starbucks.
The gay marriage bill is Senate Bill 6239.