Congress overwhelmingly approved legislation Tuesday mandating the disclosure of a trove of government files related to sex offender Jeffrey Epstein , a milestone in a long-running fight that divided President Trump’s MAGA movement.

The House voted 427-1 to pass the measure , after a band of Republicans bucked party leaders and joined with Democrats to force the matter past the opposition of GOP leadership. Hours later, Senate Minority Leader Chuck Schumer (D., N.Y.) made a motion to pass the measure by unanimous consent when it is transmitted from the House. No senator objected, putting the bill on track to be sent directly to Trump’s desk.

Epstein survivors and their backers in Congress fought “so hard against the most powerful people in the world, even the president of the United States, in order to make this vote happen today,” said Rep. Marjorie Taylor Greene (R., Ga.), whom Trump tagged as a traitor over her push to release the files. “These survivors deserve full transparency. Every document, every truth, every name,” she said.

Trump has blasted the effort, saying it was Democratic-driven and designed to embarrass Republicans and distract from GOP policy wins. But as it became clear that dozens of Republicans were likely to break ranks and support the measure to force the Justice Department to release documents, he reversed course . He said in recent days he supported passage of the bill and would sign it into law if it got to his desk, while continuing to call it a “hoax.”

Trump’s comments cleared the way for almost all Republicans to vote in favor of the measure, including House Speaker Mike Johnson (R., La.), who had criticized the effort and the GOP renegades. Johnson has pointed to progress being made by the House Oversight Committee in revealing documents from the Epstein estate, and he said he hoped the Senate would make changes related to privacy and other matters he cast as critical fixes. The Senate made no amendments.

The one lawmaker to vote against the House measure was Rep. Clay Higgins (R., La.), who cited concerns about information regarding innocent people being revealed.

Ahead of the House vote, survivors of Epstein’s abuse as teenagers held a press conference Tuesday alongside Greene and other main bill proponents, Reps. Thomas Massie (R., Ky.) and Ro Khanna (D., Calif.). Victims expressed frustration with past Democratic and Republican administrations’ lack of action but particularly targeted Trump and GOP lawmakers, for what they saw as their efforts to block or slow down the files’ release.

“Your career is in front of you, and that choice will follow you,” said Haley Robson to lawmakers, while holding a photo of herself as a child. Another Epstein victim, Jena Lisa Jones, added: “I’m begging you, President Trump, stop making this political.”

Later, dozens of Epstein victims filled rows of seats in the public galleries just above the Democratic side of the House floor. As the vote started, some of the women hugged. They cheered and clapped when the result was announced.

Sky Roberts, the brother of Virginia Giuffre, a prominent Epstein victim who died by suicide earlier this year, was emotional as he and his wife, Amanda, emerged from the successful vote. “We miss Virginia,” Amanda Roberts said. “This is what she’s been fighting for.”

Trump has said he cut off ties with Epstein long before the financier was first arrested in 2006. Epstein pleaded guilty to soliciting a minor for prostitution in 2008. Trump and Epstein socialized together in the 1990s and early 2000s. Trump later banned Epstein from his Mar-a-Lago club, the White House has said. Epstein died in 2019 in jail after he was arrested a second time and charged with sex trafficking conspiracy.

Trump, in comments to reporters Tuesday, said he has “nothing to do with Jeffrey Epstein. I threw him out of my club many years ago because I thought he was a sick pervert, and I guess I turned out to be right.”

Democrats highlighted Trump’s last-minute decision to support the bill.

“He’s caved. It’s a complete and total surrender,” said House Minority Leader Hakeem Jeffries (D., N.Y.).

Ahead of Schumer’s move to fast-track the legislation, Senate Majority Leader John Thune (R., S.D.) rejected the idea that the Senate might amend the measure. “I think when a bill comes out of the House 427-1, and the president said he’s going to sign it, I’m not sure that is in the cards,” he said. A senior administration official said that Trump would sign the measure when it arrives at the White House.

Bill supporters aired concerns that the Justice Department might not fully comply if the measure becomes law. Justice Department officials could cite a number of reasons why the material should stay under wraps, but it wasn’t clear whether they would do so. A department spokesman didn’t respond to a request for comment.

The Justice Department could also cite as a continuing investigation a review Trump recently ordered into Epstein’s relationship with former President Bill Clinton and other Democrats.

Heading into Trump’s second term, many MAGA supporters were demanding further disclosures in the Epstein case, thinking there was a list of powerful men whose identities were being protected. Earlier this year, Bondi told Fox News that a list of Epstein’s clients was “sitting on my desk right now to review.”

In July, the Justice Department backtracked on Bondi’s pledge to release more files, saying that after an “exhaustive review,” it had found no “incriminating client list” or additional documents warranting public disclosure. Amid pressure on Capitol Hill, the House Oversight Committee over the summer sent subpoenas to the Justice Department and the Epstein estate seeking documents related to Epstein.

The discharge petition put forth in early September by Massie picked up all Democrats and four Republicans—Massie and Greene, plus Reps. Nancy Mace of South Carolina and Lauren Boebert of Colorado. It reached its 218th signature earlier this month, after the long delayed swearing-in of Rep. Adelita Grijalva (D., Ariz.). Her signature showed the proposal had the support of a majority of the House and triggered the vote held Tuesday.

Johnson said legislation amounted to “a political show vote” by Democrats, who were trying “to tie President Trump somehow into this wretched scandal.” He said the bill has insufficient privacy protections for victims who haven’t stepped forward publicly. The lives of victims and other innocent people “would be made to suffer more harm if Congress is not careful in what we’re doing,” Johnson said.

Higgins—the lone lawmaker to oppose the measure—argued that a “broad reveal of criminal investigative files, released to a rabid media, will absolutely result in innocent people being hurt.”

Backers of the bill said it has sufficient protections, and the legislation allows the attorney general to redact or withhold information that would identify victims. Massie, who went into the House gallery to take selfies with Epstein victims, called the objections a “red herring,” noting the support from the survivors for the legislation.

Critics “are afraid that people will be embarrassed,” said Massie. “Well, that’s the whole point here.”

Write to Katy Stech Ferek at katy.stech@wsj.com , Siobhan Hughes at Siobhan.hughes@wsj.com and Anvee Bhutani at anvee.bhutani@wsj.com