The move came after the opposition Conservative Party said it would force a vote in parliament on Wednesday calling for the release of emails and other messages related to Mandelson's appointment in 2024.
Critics say he should never have been given the job because his relationship with Epstein - though not its extent - was known at the time.
The government has agreed to release the requested information unless it is "prejudicial to UK national security or international relations." It's unclear how much material will be released, or when.
Mandelson, 72, was fired in September from his job as envoy in Washington after emails were published showing he maintained a friendship with Epstein after the late financier's conviction for sex offences involving a minor.
This week he resigned from the House of Lords and faces a police investigation for alleged misconduct in public office, after a trove of documents released by the US Department of Justice suggested Mandelson may have shared sensitive information with Epstein when he was government minister a decade and a half ago.
The reports of an investigation emerged after Prime Minister Keir Starmer's government handed material to the police to investigate whether Mandelson leaked information to Epstein during the financial crash.
Starmer â� told his ministers that Mandelson's alleged leaks to Epstein were "disgraceful."
In 2009 he appears to have told Epstein he would lobby other members of the government to reduce a tax on bankers' bonuses, and passed on an internal government report discussing a potential sale of UK government assets.
The following year he appears to have tipped off Epstein about an imminent bailout of the European single currency.
The newly released files also suggest that in 2003-2004, Epstein sent three payments totalling $US75,000 to accounts linked to Mandelson or his partner Reinaldo Avila da Silva.
The Times newspaper, citing a government source, said officers were expected to interview Mandelson and take statements from senior Labour figures, including former prime minister Gordon Brown.
Misconduct in public office carries a maximum sentence of life in prison. Opening an investigation does not mean Mandelson will be arrested, charged or convicted.
An email requesting comment on the documents was sent to Mandelson through the House of Lords.
Epstein died by suicide in a jail cell in 2019, while awaiting trial on US federal charges accusing him of sexually abusing dozens of girls.
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