The state House of Representatives, considered the tougher of the two chambers for the measure, voted 75-59 Thursday, passing the bill that would allow same-sex marriage. Four Republicans joined an overwhelming majority of Democrats voting in favor.
Senate leaders said they have enough votes to pass the bill, which could be considered Monday, the St. Paul Pioneer Press reported.
Gov. Mark Dayton has said he will sign it into law.
In the 2012 election, Minnesotans defeated an effort to constitutionally state marriage was between a man and a woman.