The former prince, 65, had hoped to stay at Royal Lodge, his Windsor home of decades, for longer, the Sun newspaper said, but was moved under the cover of darkness on Monday and driven to a cottage in Sandringham, the King's Norfolk estate.
A royal source confirmed on Wednesday that he was now resident there, but that he might occasionally return to Windsor in the coming weeks while a transitionary phase was completed.
"With the latest batch of Epstein files it was made clear to him that it was time to go," the Sun quoted a friend as saying.
"Leaving was so humiliating for him that he chose to do it under the cover of darkness."
The King has also said that his sympathy is with the victims of abuse.
New files related to Epstein published by the US Justice Department last Friday included emails suggesting that Mountbatten-Windsor maintained regular contact with Epstein for more than two years after he was found guilty of child sex crimes.
They also include pictures appearing to show Mountbatten-Windsor crouching over and touching the waist of an unidentified woman lying on the floor. Her face was blacked out in the redacted images.
The former Duke of York has denied wrongdoing in connection with Epstein and had previously denied maintaining ties with the financier after Epstein's 2008 conviction, apart from a 2010 visit to New York to end their relationship.
Epstein died by suicide in 2019 in a Manhattan jail while awaiting trial on sex trafficking charges.
