The High Court heard in London on Thursday that the photos were "of and into the living area and dining area of the home and directly into the bedroom".
According to 7News, Harry's lawyers told Mr Justice Warby the pictures, which were "published by the Times newspaper and elsewhere online", had "very seriously undermined the safety and security of the Duke and the home".
Harry's lawyer read a statement on the new father's behalf, who was not present in court.
The statement said that Harry and wife Meghan Markle chose the home in Oxfordshire because of "the high level of privacy it afforded", but now felt "they are no longer able to live at the property".
According to 7News, the agency has agreed to pay a substantial sum in damages and legal costs and has apologised to the Duke and Duchess of Sussex.