House Bill 4127 strips out language in state law defining marriage as between a husband and wife and instead says it is simply between two individuals.
A federal judge in 2014 struck down the Oregon constitutional provision banning same-sex marriage. More than 3,400 gay and lesbian couples have officially tied the knot since then.
Last year, the U.S. Supreme Court ruled that same-sex couples throughout the country have a constitutional right to marry.
The Senate sent the bill to Gov. Kate Brown on an 18-11 vote Thursday, although no one spoke against it on the floor. The House had earlier approved the measure on a 43-13 vote.
All of the opposition came from Republicans.