WASHINGTON — Congress approved bipartisan legislation on Thursday barring the use of forced arbitration to address sexual assault and harassment claims in the workplace, sending President Biden a measure aimed at ending a secretive practice often used to shield perpetrators from full and public accountability.

The Senate passed the measure by a voice vote, clearing the bill three days after it had been approved overwhelmingly by the House. It could prompt a sea change in the way that businesses handle allegations of sexual abuse, and it was hailed by employment lawyers as one of the most significant changes to labor law in decades. The White House has indicated that Mr. Biden will sign it.

The bill’s swift passage was also the latest sign of an effort by Democratic leaders in Congress, on the heels of a series of legislative failures on the central elements of their domestic agenda, to recalibrate their approach to focus on narrower issues that generate bipartisan support.

“The differences between the parties are real and cannot be ignored,” Senator Chuck Schumer, Democrat of New York and the majority leader, said before the bill passed. But he added that lawmakers also could not “ignore the genuine chances for progress when both parties agree to move forward on certain topics.”

On Tuesday, the House passed the most significant overhaul of the United States Postal Service in nearly two decades as well as a stopgap spending bill to avert a government shutdown. And on Wednesday, a bipartisan group of senators put forth new legislation to reauthorize the Violence Against Women Act, which they said was close to finding the 60 votes that would be needed to pass in the Senate.

“We now have a series of bipartisan bills moving forward,” said Mr. Schumer, who moved on Thursday to bring the postal overhaul to a vote in the Senate.

The forced arbitration bill brought together an unlikely coalition of liberals and conservatives. It would give survivors of sexual harassment and assault the ability to sue their abusers in state, tribal or federal court, even if a survivor had signed an employment agreement that barred such lawsuits and required misconduct claims to be settled through arbitration.

An estimated 60 million American workers are subject to such agreements, and they have attracted attention in the years following the #MeToo movement as a major reason that it is difficult to penalize sexual abusers for their offenses. The secretive arbitration process can weigh heavily in favor of protecting perpetrators of abuse, affording victims no chance to seek accountability, proponents of the bill said.

“We are giving these workers a new path to justice,” said Senator Kirsten Gillibrand, Democrat of New York, who proposed the bill with Senator Lindsey Graham, Republican of South Carolina, in 2017.

“The bill is going to help fix a broken system,” she said at a news conference following its passage.

Mr. Graham said the measure would force businesses to “up their game,” comparing sexual harassment and assault in the workplace to a worker losing a finger on the job.

“I’m a limited-government Republican, but there’s a place for the government when it comes to our daily lives,” Mr. Graham said after the vote.

He said he hoped the legislation would be a model for more bipartisan work in the Senate. “There’s plenty of things we can do that are meaningful like this,” he said.

At the news conference, Mr. Graham and Mr. Schumer congratulated a tearful Gretchen Carlson, the former Fox News anchor whose lawsuit against Roger Ailes, the former chairman of Fox News, brought public attention to the issue of forced arbitration.

“You started it,” Mr. Schumer told her. “You had courage.”

Some Republicans were opposed to the bill, arguing that the federal government had no place reaching into employment contracts and invalidating them. But the legislation generated such broad support that none of them insisted on officially registering their objections, allowing the legislation to pass without a recorded vote.

Such an outcome is a rarity in today’s Senate, where the two parties have sparred bitterly over policy and Republicans have wielded the filibuster to block much of Mr. Biden’s agenda.

The flurry of legislative activity this week follows a torturous few months on Capitol Hill for the president and his party. Democrats saw their push for voting rights legislation stymied by a Republican blockade, and they failed to reach consensus in their own ranks to push through a $2.2 trillion social safety net and climate change package over unified Republican opposition.