The 66-year-old, who was being held without bail in a Manhattan jail, was accused of abusing dozens of underage girls as young as 14 in New York and Florida.
Epstein, who denied the charges, was found at 6.30am on Saturday morning, according to a statement from the Department of Justice.
Officials speaking anonymously said he had hanged himself.
Attorney General William Barr, in announcing the investigation by the FBI and the Justice Department's inspector general's office, said he was "appalled" to learn of Epstein's death while in federal custody.
"Mr Epstein's death raises serious questions that must be answered," he said in a statement.
The fire department said it received a call at 6.39am that Epstein was in cardiac arrest and he was pronounced dead at New York-Presbyterian Lower Manhattan Hospital.
AP reports the medical examiner's office has confirmed his death.
The statement from the Department of Justice said Epstein was found unresponsive in his cell from an apparent suicide, adding that life-saving measures were immediately initiated by responding staff.
Emergency medical services were requested and Epstein was transferred to hospital for treatment, before being pronounced dead.
NBC News is reporting that, contrary to earlier reports, Epstein was not on suicide watch at the time he was found.
He was facing 45 years in prison if convicted.
Last month, Epstein had reportedly been found unconscious with neck injuries on the floor of his cell. His lawyers declined to comment at the time.
A source said he had recently been taken off suicide watch, but it is not clear when.
According to the Bureau of Prisons, he had been in the jail's special housing unit, a heavily secured part of the prison, which separates high-profile inmates from the general population.
It was the same unit where drug lord Joaquin "El Chapo" Guzman was held until he moved to the Supermax prison in Colorado.
Epstein pleaded guilty in 2008 to prostitution-related charges involving underage girls, in exchange for the Justice Department's agreement not to prosecute him on similar charges.
He served 13 months in jail and agreed to register as a sex offender under the 2008 plea deal, which is now widely seen as too lenient. Federal prosecutors in New York had reopened the case after reports from the Miami Herald stirred outrage.
His lawyers had argued the agreement barred federal prosecutors in Manhattan from pursuing the latest case over the same conduct.
However, US Attorney Geoffrey Berman said there was no such block.
Alexander Acosta, the US Labour Secretary, resigned last month after criticism for overseeing the deal when he had been US attorney in Miami.
Epstein had also been appealing Mr Berman's denial of his request to remain under house arrest in his $77m (£64m) mansion on Manhattan's Upper East Side while awaiting trial.
Accuser Jennifer Araoz said: "We have to live with the scars of his actions for the rest of our lives, while he will never face the consequences of the crimes he committed, the pain and trauma he caused so many people."
Brad Edwards, a lawyer for near two dozen other accusers, said it was "not the ending anyone was looking for".
He said: "The victims deserved to see Epstein held accountable, and he owed it to everyone he hurt to accept responsibility for all of the pain he caused."
His death comes as court papers were unsealed in which a woman claimed Prince Andrew had touched her breast at Epstein's Manhattan mansion.
Buckingham Palace said claims made by Johanna Sjoberg against Prince Andrew, a former friend of Epstein, were categorically untrue.
On Friday, more than 2,000 pages of a settled lawsuit against Epstein's ex-girlfriend were released by accuser Virginia Giuffre.
They include graphic allegations against Epstein as well as the transcript of a 2016 deposition in which he refused to answer any questions to avoid incriminating himself.
Epstein also had links with Donald Trump. Video of them together at a party in 1992 emerged in June, and they were pictured together five years later too.
There is no suggestion that there was any criminal wrongdoing taking place at the party and Mr Trump now claims he never liked Epstein.
:: Anyone feeling emotionally distressed or suicidal can call Samaritans for help on 116 123 or email [email protected] in the UK. In the US, call the Samaritans branch in your area or 1 (800) 273-TALK.