Washington CNN  — 

The Senate on Tuesday passed legislation to protect same-sex and interracial marriage, called the Respect for Marriage Act, in a landmark bipartisan vote.

The final vote was 61-36. The bill was supported by all members of the Democratic caucus and 12 Republicans, the same dozen GOP members who backed the bill for a procedural vote earlier this month.

The House will now need to approve the legislation before sending it to President Joe Biden’s desk to be signed into law. The House is expected to pass the bill before the end of the year – possibly as soon as next week.

“For millions of Americans, this legislation will safeguard the rights and protections to which LGBTQI+ and interracial couples and their children are entitled,” Biden said in a statement Tuesday evening after Senate passage, hailing it as a “bipartisan achievement.”

While the bill would not set a national requirement that all states must legalize same-sex marriage, it would require individual states to recognize another state’s legal marriage.

So, in the event the Supreme Court might overturn its 2015 Obergefell v. Hodges decision that legalized same-sex marriage, a state could still pass a law to ban same-sex marriage, but that state would be required to recognize a same-sex marriage from another state.

The legislation cleared a key procedural hurdle earlier this month, when the Senate voted 62-37 to break a filibuster.

The bipartisan group, which includes Republican Sens. Rob Portman of Ohio, Susan Collins of Maine and Thom Tillis of North Carolina and Democratic Sens. Tammy Baldwin of Wisconsin and Kyrsten Sinema of Arizona, previously said in a statement that they looked “forward to this legislation coming to the floor.”

Senate Majority Leader Chuck Schumer cited those five senators for their “outstanding and relentless work” on this landmark legislation during a floor speech Tuesday morning.

“For millions and millions of Americans, today is a very good day,” he said. “An important day. A day that’s been a long time coming.”

In a sign of how much support has grown in recent years for same-sex marriage, the bill found backing from GOP senators including those in deeply red states.

Republican Sen. Cynthia Lummis of Wyoming told CNN’s Manu Raju earlier this month that she voted to advance the Senate’s same-sex marriage bill due to “Article 1, Section 3 of the Wyoming Constitution,” which she read to reporters and includes an anti-discrimination clause.

“That’s why we’re called the equality state,” she added.

Utah Sen. Mitt Romney, meanwhile, said the “bill made sense” and “provides important religious liberty protections.”

“While I believe in traditional marriage, Obergefell is and has been the law of the land upon which LGBTQ individuals have relied,” Romney said in a statement. “This legislation provides certainty to many LGBTQ Americans, and it signals that Congress – and I – esteem and love all of our fellow Americans equally.”

This story and headline have been updated with additional developments Tuesday.

CNN’s Alex Rogers and Paul LeBlanc contributed to this report.