Friday's move comes two days after a congressional committee released thousands of documents that raised new questions about Trump's relationship with the late financier, and marks the latest in a series of demands by Trump for federal law enforcement to pursue his perceived political enemies.
Attorney-General Pam Bondi said Jay Clayton, the top federal prosecutor in Manhattan, will lead the investigation.
The Epstein scandal has been a political thorn in Trump's side for months, partly because he amplified conspiracy theories about Epstein to his own supporters. Many Trump voters believe Bondi and other Trump officials have covered up Epstein's ties to powerful figures and obscured details surrounding his death by suicide in a Manhattan jail in 2019.
Trump has harnessed the Justice Department to target other perceived political enemies, notably former FBI Director James Comey and New York State Attorney-General Letitia James, both of whom were charged after Trump replaced the prosecutor leading the cases.
Legal experts say Trump's demands could undermine the criminal cases that emerge from those probes, as judges can dismiss cases found to be motivated by "vindictive prosecution" - which both Comey and James have raised, though judges have not yet ruled on their requests to dismiss the cases.
Along with Clinton, who socialised with Epstein in the early 2000s, Trump said he had asked the Justice Department to investigate former Treasury Secretary Larry Summers, and Reid Hoffman, the LinkedIn founder who is also a prominent Democratic donor. All three men were mentioned in the 20,000 Epstein-related documents released by the House Oversight Committee on Wednesday.
"Epstein was a Democrat, and he is the Democrat's problem, not the Republican's problem!" Trump wrote on social media.
"They all know about him, don't waste your time with Trump. I have a Country to run!"
JPMorgan said in a statement the US bank regrets its past association with Epstein, who was a client between 1998 and 2013, and did not help him commit "heinous acts."
The Justice Department's decision to acquiesce to Trump's demand came despite a July memo in which the department and the FBI said there was no "evidence that could predicate an investigation against uncharged third parties" in the Epstein case.
"This systematic review revealed no incriminating 'client list,'" the memo said.
"There was also no credible evidence found that Epstein blackmailed prominent individuals as part of his actions."
Trump and Epstein were friends during the 1990s and the 2000s, but Trump says he broke off ties before Epstein pleaded guilty in 2008 to charges of soliciting a minor for prostitution.
Trump has consistently denied knowing about the late financier's abuse and sex trafficking of underage girls. Still, some of Trump's most ardent supporters have accused his administration of a cover-up. Trump, who frequently engages with reporters, has declined to take questions over the last several days as new revelations about Epstein have become public.
The Republican-controlled House of Representatives is expected to vote next week on legislation that would force the Justice Department to release all of the material it holds on Epstein, who was facing federal charges of sex trafficking minors at the time he took his own life.
The measure is expected to pass, even after House Speaker Mike Johnson repeatedly manoeuvred to try to block the vote. It would also require the Senate to pass similar legislation and Trump's approval to compel the Justice Department to act
No credible evidence has surfaced that Clinton, Summers or Hoffman were involved in Epstein's sex trafficking. All have previously denied wrongdoing and have expressed regret about their relationships with him.
