The undated photograph has been unearthed as part of the US department of justice's Epstein-related document dump earlier this year.
In the image, first reported by ITV News, Mountbatten-Windsor, the King's disgraced brother, and Mandelson appear to be sitting outside at a wooden table and have mugs with a US flag on them in front of them.
The broadcaster said the picture was taken in Martha's Vineyard - an island in Massachusetts.
It is believed to be the first photograph of the two men with Epstein that has been uncovered.
Both men are wearing white bathrobes, in an image that bears a resemblance to one previously discovered of Mandelson, which could be seen in Epstein's "birthday book".
The birthday book image of Mandelson, which also shows him in a bathrobe, is accompanied by a message in which he describes the disgraced financier as his "best pal".
Mountbatten-Windsor, the former Duke of York, and Mandelson have been arrested on suspicion of misconduct in public office over their connections with the paedophile and have both since been released under investigation.
Both men feature a number of times in the so-called Epstein files, including images of Mountbatten-Windsor bent over an unidentified female and lying across the laps of a number of women.
Images of Mandelson receiving a foot massage and others of him standing in his underwear have also been published by the US Department of Justice.
Both Mountbatten-Windsor and Mandelson have denied any wrongdoing over their association with Epstein.
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