A lawyer for Epstein's estate confirmed to the BBC that the two islands - Little St James and Great St James - have been listed.
Lawyer Daniel Weiner said some proceeds from the sale will be used to settle outstanding lawsuits.
Epstein died in jail in 2019, awaiting trial on sex trafficking charges.
The financier bought the 90-acre Little St James - the more developed of the two - nearly 25 years ago for almost $8m (£6m).
He then acquired the larger Great St James in 2016 for $22.5m and had drawn up plans to develop the 161-acre island by building homes, an amphitheatre, as well as an underwater office and pool.
Bespoke Real Estate, which is jointly overseeing the sale, told the BBC both islands are being offered for a total $125m.
Epstein was accused by US Virgin Islands attorney general Denise George of sexually abusing girls as young as 12 years old on Little St James.
The lawsuit, filed two years ago, also claimed that one 15-year-old girl attempted to escape the island by swimming away before being captured and having her passport confiscated.
Mr Weiner, a partner at New York law firm Hughes Hubbard & Reed, said the sale is taking place with the support of Ms George and that the proceeds "will be used by the estate for the resolution of outstanding lawsuits and the regular costs of the estate's operations".
Epstein reportedly welcomed a number of high profile guests to Little St James over the years. One of Epstein's alleged victims, Virginia Giuffre, claimed in a civil suit that Prince Andrew had abused her on the island. Prince Andrew denied the claims and said he had no recollection of meeting Ms Giuffre.
The prince recently paid a settlement to Ms Giuffre to end a civil case in the US. The settlement accepted no liability and Prince Andrew has always strongly rejected claims of wrongdoing.
Other visitors to Little St James included Jes Staley, the former boss of Barclays.
He resigned from the UK bank last year following an investigation by financial regulators over how the banker had characterised his relationship with Epstein.
Mr Staley dropped by Epstein's island in 2015 a few months before he took on the chief executive role at Barclays.
UK financial regulators began an investigation after JP Morgan - Mr Staley's former employer - handed over 1,200 emails sent between the banker and Epstein mostly 2008 and 2012.
Regulators were concerned that the emails showed a closer relationship between the two men than Mr Staley had described to Barclays board.
Mr Staley is contesting the regulators' finding.