The King acted to stem mounting public disapproval as more damning details emerged about Andrew's relationship with the convicted sex offender.
Charles moved to preserve the monarchy from the fallout by forcibly removing a British prince's title for the first time in a century.
The former Prince Andrew will now be known as Andrew Mountbatten Windsor.
He will move out of Royal Lodge, the 30-room mansion near Windsor Castle where he has lived for more than 20 years, and into a more remote home funded by his brother on the Sandringham Estate in eastern England.
The British government welcomed the King's decision.
"We warmly, I warmly support what the King is doing today," trade minister Chris Bryant told the BBC.
"I think the vast majority of people in this country will think that it's the right thing to do."
Andrew surrendered his use of the title Duke of York earlier in October over new revelations about his friendship with Epstein and renewed sexual abuse allegations by Giuffre, whose posthumous memoir was published last week.
Andrew denies all her claims.
But the King went even further to punish him for serious lapses of judgment by removing the title of prince that he has held since birth as a child of a monarch, the late Queen Elizabeth II.
"These censures are deemed necessary, notwithstanding the fact that he continues to deny the allegations against him," the palace said.
"Their majesties wish to make clear that their thoughts and utmost sympathies have been, and will remain with, the victims and survivors of any and all forms of abuse."
A British prince or princess was last stripped of their title in 1919, when Prince Ernest Augustus, who was a UK royal and also a prince of Hanover, had his British title removed for siding with Germany during World War I.
Giuffre's family declared victory on behalf of Andrew's accuser, who died by suicide in April at age 41.
She said that in the early 2000s, when she was a teenager, she was caught up in Epstein's sex-trafficking ring and exploited by Andrew and other influential men.
Epstein was found dead in a New York jail cell in 2019 in what investigators described as a suicide.
"Today, an ordinary American girl from an ordinary American family, brought down a British prince with her truth and extraordinary courage," Giuffre's family said in a statement.
Her brother Sky Roberts said Andrew should face further investigation, telling the BBC "he needs to be behind bars, period".
Bryant said Andrew was now an "ordinary member of the public" and should go to the US to answer questions about Epstein if asked.
Andrew could face legal trouble in Britain, where police are probing a claim he asked one of this police bodyguards to dig up dirt on Giuffre.
A committee of British MPs is also looking into how Andrew paid for Royal Lodge, which he leased for a nominal annual fee.
Andrew faced a new round of public outrage after emails emerged earlier in October showing he had remained in contact with Epstein longer than he previously admitted.
That news was followed by publication of Nobody's Girl, by Giuffre, who alleged she had sex with Andrew when she was 17.
Andrew, 65, has long denied Giuffre's claims, but stepped down from royal duties after a disastrous 2019 BBC interview in which he attempted to rebut her allegations.
Andrew paid millions in an out-of-court settlement in 2022 after Giuffre filed a civil suit against him in New York.
While he did not admit wrongdoing, he acknowledged Giuffre's suffering as a victim of sex trafficking.
