The vote is expected as soon as Tuesday after Trump's reversal on Sunday, days after a House petition gathered enough support to force a vote, a rare instance of House Republicans defying the president's wishes.
Until the weekend, Trump and his staff had lobbied hard to prevent any further release of files from the criminal investigation by the US Department of Justice into Epstein, a wealthy New York financier who was, for a time, friends with Trump.
"House Republicans should vote to release the Epstein files, because we have nothing to hide," the Republican president wrote late on social media.
"And it's time to move on from this Democrat Hoax perpetrated by Radical Left Lunatics in order to deflect from the Great Success of the Republican Party."
Democrats, and even some of Trump's supporters, say there is nothing hoax-like in the release of authentic Justice Department records.
Epstein was convicted on several Florida state and federal charges related to his sexual abuse and trafficking of teenaged girls. He died in a federal jail cell in Manhattan in 2019 in what was ruled a suicide, a few weeks after he was arrested on new federal charges of sex trafficking children.
California Representative Robert Garcia, the senior Democrat on the House Oversight Committee, said Trump "has tried everything to kill our Jeffrey Epstein investigation".
"And now he's panicking and has realised he is about to lose this Epstein vote to force the Department of Justice to release the files."
Trump announced his change of heart because he had grown exasperated with Republicans' fixation on the Epstein files and wanted them to focus on the cost of living and other issues that matter more to voters, a senior White House official said, speaking on condition of anonymity.
House Speaker Mike Johnson said he believed a vote on releasing the files should help put to rest allegations that Trump had any connection to Epstein's abuse.
"He's never had anything to hide," Johnson told reporters on Monday, referring to Trump.
"He and I had the same concern, that we wanted to ensure that victims of these heinous crimes are completely protected from disclosure, those who don't want their names to be out there."
If the House passes the resolution, it would move to the Senate, which would also need to vote on it before sending it to Trump to sign.
Trump partied with Epstein in New York and Florida's Palm Beach in the 1990s and 2000s, along with other members of the US and international power elite.
The president has said his friendship with Epstein ended some time in the 2000s and he had no connection to Epstein's crimes, and that his political enemies are trying to smear him by insinuating otherwise.
Emails released last week by a House committee showed the disgraced financier believed Trump "knew about the girls", though it was not clear what that phrase meant. The White House said the released emails contained no proof of wrongdoing by Trump.
Meanwhile Former US Treasury Secretary Larry Summers will step back from all public commitments, days after Trump ordered the Justice Department to investigate his and other prominent Democrats' ties to Epstein.
Summers, a former president of Harvard University, where he is a professor, told the university's student newspaper that the move was to allow him "to rebuild trust and repair relationships with the people closest to me."
"I am deeply ashamed of my actions and recognise the pain they have caused. I take full responsibility for my misguided decision to continue communicating with Mr. Epstein," Summers told The Crimson.
Summers, a Democrat, served as former President Bill Clinton's Treasury Secretary and former President Barack Obama's National Economic Council director.
