The family of Andrew's late accuser Virginia Giuffre said she "brought down a British prince with her truth and extraordinary courage” after he was stripped of all his titles.
The King took the dramatic decision on Thursday to formally remove his brother Andrew of his Prince and Duke of York titles and HRH style, a move that ends his public life.
The disgraced royal whose friendship with convicted paedophile financier Jeffrey Epstein led to his downfall will effectively have the status of a commoner and will be known as Andrew Mountbatten Windsor.
Andrew had tainted the reputation of the royal family with his association with Epstein and for many years was dogged by allegations he sexually abused Virginia Giuffre after she was trafficked by the financier. He has strenuously denied the allegations.
Ms Giuffre, who took her own life earlier this year, repeatedly claimed she had sex with Andrew as a teenager.
In a statement Ms Giuffre’s family said: "Today, an ordinary American girl from an ordinary American family brought down a British prince with her truth and extraordinary courage.”
They said she “never stopped fighting for accountability for what had happened to her and countless other survivors like her.”
"Today, she declares a victory. We, her family, along with her survivor sisters, continue Virginia's battle and will not rest until the same accountability applies to all of her abusers and abetters, connected to Jeffrey Epstein and Ghislaine Maxwell."
Sigrid McCawley, a lawyer for Virginia Giuffre during her civil sex assault case against Prince Andrew, which he settled out of court, said the King stripping Andrew's titles was a "tipping point".
She said: "The voice of Virginia Giuffre has changed history. Her bravery, determination and resilient spirit has led to this defining moment.
"As we account for the tipping point significance of the King stripping the title "Prince" from his brother Andrew, it should be a lesson for all to listen, hear and believe survivors of abuse."
The monarchy was coming under increasing pressure to resolve the issues around Andrew, with foremost his property arrangements, amid growing calls for him to give up Royal Lodge after it emerged he was paying a "peppercorn" rent for his 30-room mansion.
Buckingham Palace said in a statement: "His Majesty has today initiated a formal process to remove the style, titles and honours of Prince Andrew.
"Prince Andrew will now be known as Andrew Mountbatten Windsor. His lease on Royal Lodge has, to date, provided him with legal protection to continue in residence.
"Formal notice has now been served to surrender the lease and he will move to alternative private accommodation. These censures are deemed necessary, notwithstanding the fact that he continues to deny the allegations against him.
"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."
It is understood the unprecedented move was taken by the King in light of the serious lapses in judgment his brother made and Charles was supported in his decision by the royal family including the Prince of Wales, with Andrew not objecting.
William was put in an untenable position when he appeared to be ambushed by Andrew during the Duchess of Kent's recent funeral, with the disgraced royal tried to talk to his nephew, who barely acknowledged him.
Andrew will move as soon as practicable to an undisclosed property on the King's Sandringham estate in Norfolk, with the accommodation privately funded by the King, who will also make private financial provisions for his brother.
Sarah Ferguson lived with her ex-husband Andrew at Royal Lodge but will not be housed by Charles and will have to find a new home.
