The revelations emerged in legal documents submitted by his brother as part of his own legal battle with the publisher, which has returned to the high court on Tuesday for a three-day hearing.
Harry is suing the publishers, alongside actor Hugh Grant, over alleged unlawful information gathering at its titles.
His lawyer David Sherborne told the court his attempts to seek an apology from Rupert Murdoch’s company over phone hacking were carried out with the approval of his grandmother the late Queen Elizabeth II.
Details of William’s settlement were published in legal documents submitted by his brother.
READ MORE: Prince Harry will use King Charles’s Coronation to ‘get new snaps with the Royal Family’
Harry said that the Royal Family was “incredibly nervous” but wanted to “avoid the situation where a member of the Royal Family would have to sit in the witness box and recount the specific details of the private and highly sensitive voicemails that had been intercepted by [the News of the World royal reporter] Clive Goodman”.
The Royal Family, according to Harry, wanted to avoid causing any “reputational damage” – like when “published details” emerged from the now-King’s “intimate telephone conversation” with the now-Queen Consort in 1989.
Despite being included in the documents, there are no further details about what the alleged settlment.
There are also no details as to whether it related to the Sun or the News of the World, which was closed down at the height of the phone-hacking scandal in 2011.
Last month, Prince Harry was one of a host of high-profile people suing another publisher Associated Newspapers over claims that they were the victims of phone hacking and other serious privacy breaches.
Prince Harry returned to the UK at the end of March to attend the High Court in London. Celebrities such as Sir Elton John were also in attendance.
The Duke of Sussex is expected to appear in court in the UK after the Coronation for a trial against another publisher.