"This is not just a victory for her, but for every single survivor of the horrific crimes perpetrated by [Jeffrey] Epstein and his co-conspirators," the family said in a statement.
Andrew will no longer be known as the Duke of York, in a move which finally completes his banishment from royal life.
However, he will remain a prince, having been born the son of Queen Elizabeth II.
His former wife, Sarah Ferguson, will also no longer use her title of The Duchess of York, it is understood.
In a statement, Prince Andrew said: "In discussion with The King, and my immediate and wider family, we have concluded the continued accusations about me distract from the work of His Majesty and the Royal Family.
"I have decided, as I always have, to put my duty to my family and country first. I stand by my decision five years ago to stand back from public life.
Follow updates: Prince Andrew latest: 'I must go a step further'
"With His Majesty's agreement, we feel I must now go a step further. I will therefore no longer use my title or the honours which have been conferred upon me.
"As I have said previously, I vigorously deny the accusations against me."
King 'glad' of the outcome
The decision comes following increased pressure on Prince Andrew after continuing reports of his relationship with paedophile financier Jeffrey Epstein, and his relationship with an alleged Chinese spy.
It is understood that the change will take effect immediately.
The King is glad of the outcome, it is understood, and the decision was taken in close consultation with His Majesty and other members of the Royal Family.
Read more from Sky News:
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He will continue to be known as Prince Andrew and will continue to live at the Windsor Estate at the Royal Lodge.
The move also does not impact the position of his daughters, Princess Beatrice and Princess Eugenie.
For the second year running, he is not expected to attend the Royal Family's annual Christmas celebrations at Sandringham.
'An unwelcome distraction'
Sky News' royal correspondent, Rhiannon Mills, said: "This is quite an extraordinary move. I think it shows that, actually, things had gone too far.
"Prince Andrew, and allegations about him and Virginia Giuffre, were continuing to be too much of a distraction for the Royal Family."
Jack Royston, chief royal correspondent at Newsweek said: "This does not go far enough".
He added what was needed was: "An acknowledgement from the royal family that - irrespective of whether Prince Andrew denies the substantive allegations against him - it was morally wrong for him to grovel to Jeffrey Epstein."
The Guardian's former royal correspondent Stephen Bates said: "He's shown no sign of any sort of contrition. He continues to deny all the allegations against him. And he speaks of his duty to the family. Well, it's a bit late to be thinking about that."
What is Prince Andrew accused of?
Prince Andrew has denied allegations made by Ms Giuffre - one of Epstein's victims - of sexual assault.
She had filed a civil lawsuit against Prince Andrew, accusing him of sexually assaulting her on three occasions after she was introduced to him by Epstein.
In a 2019 interview with BBC Newsnight, he said he had no knowledge of ever meeting Ms Giuffre, claiming a well-known image of them together had been doctored.
The case was settled outside of court for a sum believed to have been around £12m.
Ms Giuffre died in April. Her family said Ms Giuffre "lost her life to suicide" at her farm in Western Australia, aged 41.
Giuffre's family: 'Victory for Virginia'
In a statement, the family of Virginia Giuffre said they supported Andrew's decision but repeated accusations that he had made misleading statements. Andrew has repeatedly denied any wrongdoing.
"We, the family of Virginia Roberts Giuffre, believe that Prince Andrew's decision to give up his titles is vindication for our sister and survivors everywhere.
"This decisive action is a powerful step forward in our fight to bring Jeffrey Epstein and Ghislaine Maxwell's child sex-trafficking network to justice.
"This moment serves as victory for Virginia, who consistently maintained, 'He knows what happened, I know what happened, and there's only one of us telling the truth, and I know that's me.'
"This is not just a victory for her, but for every single survivor of the horrific crimes perpetrated by Epstein and his co-conspirators."
Anyone feeling emotionally distressed or suicidal can call Samaritans for help on 116 123 or email jo@samaritans.org in the UK. In the US, call the Samaritans branch in your area or 1 (800) 273-TALK.
The statement comes straight from Prince Andrew, the tone of it very personal as he says he is putting his "duty to my family and country first".
But this was clearly not entirely his decision.
From the first sentence, where he says "in discussion with the King", we're left in no doubt that his brother must have said enough was enough.
Royals latest: Andrew explains decision to give up titles
The fact we're being guided that the King is glad of this outcome says it all; for the monarch and the wider family, the questions of what they were going to do about Andrew had to stop.
After years of upset caused by his association with convicted paedophile Jeffrey Epstein, he has done the family one favour by personally announcing that he will no longer use his titles.
For the King to forcibly remove them would have taken up precious parliamentary time and weeks of column inches.
To be clear his titles aren't removed, they remain extant but inactive like his HRH title.
But Prince Andrew won't use them any more and that will be humiliation enough for a man who has already been stripped of his military affiliations, his charity patronages and his ability to have any kind of public profile.
Read more:
Virginia Giuffre details accusation in posthumous book
Sarah Ferguson explains message to Epstein
This ends the questions on what more the monarch could do to show how the family felt about the accusations, the upset and the embarrassment caused.
Will it stop the stories, the allegations and the interest in Prince Andrew? That is far less certain.
But in what is the prince's first public statement since that ill-fated Newsnight interview in 2019, it is striking that he signs it off by saying: "I vigorously deny the accusations against me."
The decision is understood to have been made in close consultation with King Charles and other members of the Royal Family.
Prince Andrew, whose ex-wife Sarah Ferguson will also no longer use her Duchess of York title, said continued accusations against him were distracting from the King's work.
He had been accused by Virginia Giuffre, who died in April, of sexually assaulting her. He denies this.
Prince Andrew had also been hit by new reports of his relationship with paedophile financier Jeffrey Epstein. And a China spy controversy - In December 2024, it emerged that a "close confidant" of Andrew's was a suspected Chinese spy.
Follow updates: Prince Andrew latest: 'I must go a step further'
What titles is he giving up?
Prince Andrew is giving up his Duke of York title. Sky News understands this will be immediate.
He will also give up his knighthood as a Knight Grand Cross of the Royal Victorian Order (GCVO) and his Garter role as a Royal Knight Companion of the Most Noble Order of the Garter.
He will retain the dukedom, which can only be removed by an Act of Parliament, but will not use it.
Prince Andrew will also remain a prince, having been born the son of Elizabeth II.
What has he been accused of?
Ms Giuffre, who was one of Epstein's victims, alleged Prince Andrew sexually assaulted her on three occasions when she was 17.
In her posthumous memoir Nobody's Girl, she alleged that Prince Andrew was "entitled" and "believed having sex with me was his birthright".
Prince Andrew has always denied the allegations.
He has also always claimed that a well-known image of them together had been doctored. Before her death, which her family said was by suicide, the case was settled outside of court for a sum believed to have been around £12m.
Where will he live?
Sky News understands that he will continue to live at the Windsor Estate at the Royal Lodge.
But for the second year running he will not be attending the Royal Family's annual Christmas celebrations at Sandringham, it is understood.
Will it impact the Princesses?
The decision, which is understood to have left the King feeling glad, will not impact on the position of his daughters, Princess Beatrice and Princess Eugenie, it is also understood.
But Sky News' royal correspondent, Rhiannon Mills, explains how it may not stop the influx of negative stories about him.
She said: "This ends the questions on what more the monarch could do to show how the family felt about the accusations, the upset and the embarrassment caused.
"Will it stop the stories, the allegations and the interest in Prince Andrew? That is far less certain. But in what is the Prince's first public statement since that ill-fated Newsnight interview in 2019, it is striking that he signs it off by saying "I vigorously deny the accusations against me".
What did Prince Andrew say?
In a statement, Prince Andrew said: "In discussion with The King, and my immediate and wider family, we have concluded the continued accusations about me distract from the work of His Majesty and the Royal Family.
"I have decided, as I always have, to put my duty to my family and country first. I stand by my decision five years ago to stand back from public life.
"With His Majesty's agreement, we feel I must now go a step further. I will therefore no longer use my title or the honours which have been conferred upon me.
"As I have said previously, I vigorously deny the accusations against me."
Anyone feeling emotionally distressed or suicidal can call Samaritans for help on 116 123 or email jo@samaritans.org in the UK. In the US, call the Samaritans branch in your area or 1 (800) 273-TALK.
It comes after several local media outlets in Spain reported that Mr Andic's death was being investigated as a possible homicide.
The billionaire founder of the fashion chain reportedly slipped and fell from a 150-metre cliff while hiking in the Monserrat caves, near Barcelona, last December.
La Vanguardia newspaper reported late on Thursday that one element the judge looking into Mr Andic's death was investigating was contradictory statements Mr Andic's son Jonathan gave as a witness, and that authorities were searching his phone for more evidence.
However, the newspaper reported that, during the 10-month probe, investigators had not found any conclusive evidence linking Jonathan to his father's death.
Barcelona court's press office said on Friday that the case, which is still sealed, wasn't directed at any particular individual.
The Andic family said it expected Jonathan to be proven innocent.
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According to La Vanguardia, a statement from them read: "The Andic family has not and will not comment on Isak Andic's death in all these months.
"However, they wish to show their respect for the ongoing investigations and will continue to cooperate with the relevant authorities, as they have done so far.
"They are also confident that this process will be concluded as soon as possible and that Jonathan Andic's innocence will be proved."
Seen as a rival of Zara founder Amancio Ortega, Istanbul-born Isak Andic moved to Catalonia in northeastern Spain in the 1960s and founded Mango in 1984.
Son appointed board vice-president
At the time of his death, he was non-executive chairman of the fashion brand and worth $4.5bn (£3.6bn), according to Forbes.
Jonathan Andic was appointed vice-president of the board of the privately held company on his father's death and president of its holding company MNG.
His sisters Judith and Sarah were named as vice presidents of MNG.
Sky News has contacted Mango for a comment.
Professor Noa Eliakim-Raz, head of returning hostages at Rabin Medical Center in Petah Tikva, Israel, said returned hostages may have lost "their ability to make decisions".
On Monday, Hamas handed over all 20 surviving hostages, held in Gaza, in exchange for around 1,900 Palestinian prisoners.
But Professor Eliakim-Raz warned they face health problems that medics are treating.
'It can even be life-threatening'
Speaking to Sky News' Sally Lockwood, Professor Eliakim-Raz said: "We were concerned in the first couple of days about refeeding syndrome, which is reintroducing food after a long time if you were someone who ate a very little amount of food, especially carbohydrates, and reintroducing food can cause damage to the body.
"There are electrolytes changes and shifts in fluids in the body when you reintroduce food quickly. It's related to insulin secretion which can be dangerous. There are a spectrum of clinical syndromes but it can even be life-threatening if you don't do it very carefully."
She added that, despite the potential issues, the hostages had so far arrived in good spirits.
'In captivity you lose the ability to make decisions'
Professor Eliakim-Raz added: "When you are in captivity you lose the ability to make decisions and we try to give them back their identity.
"I totally feel it's a life-changing experience for me, I feel it has changed the way I look at very simple things in life and how I appreciate simple things in life.
"These people are coming from a place that tried to erase their identity, to erase humanity, very basic things that we feel as human beings.
"They came to the ward smiling, they know how to show appreciation, they show friendship, and that's always amazing.
'Some have social issues'
"I think as a medical profession we are obliged to give medical assistance and humanitarian terms to everyone. That's what we do and we swore to do. That's what I think should happen everywhere."
She added: "It's very different, one from the other. It depends if you were in captivity alone or in a group. If you were underground or not, how much food you got and not only how much, but how diverse it was.
"Some have more physical issues, some have social issues."