Princess Diana and Dodi Al Fayed were unlawfully killed due to the "gross negligence" of driver Henri Paul and the paparazzi, an inquest has found.
The inquest jury also specified that Mr Paul's drink-driving and a lack of seatbelts contributed to their deaths.
Princes William and Harry said they "agreed" with the verdicts and thanked the jury for the "thorough way" in which they considered the evidence.
But Mr Al Fayed's father Mohamed has refused to accept the verdict.
The jury of six women and five men returned joint verdicts of unlawful killing through grossly negligent driving - or gross negligence manslaughter, by majorities of nine to two.
The inquest into the 1997 Paris crash that killed the couple and Mr Paul lasted six months.
The total cost to British taxpayers of investigating Princess Diana's death is expected to top £10 million.
A poll of 1,000 people conducted on behalf of the BBC's Newsnight programme found 78% of people thought the estimated £10 million bill had not been well spent.
It also found the majority (62%) of those asked thought the princess's death was a tragic accident.
Princess Diana and Dodi Al Fayed were killed when Mr Paul crashed a hired Mercedes into a pillar in the Pont de l'Alma tunnel in Paris in the early hours of 31 August, 1997.
In a statement, Diana's sons William and Harry thanked the jurors.
"We agree with their verdicts and are both hugely grateful to each and every one of them for the forbearance they have shown in accepting such significant disruption to their lives over the past six months."
They also thanked the coroner, Lord Justice Scott Baker, for his "unfailing courtesy" and to former bodyguard Trevor Rees - the only survivor - who gave evidence.
"Finally, the two of us would like to express our most profound gratitude to all those who fought so desperately to save our mother's life on that tragic night."
'Blow to millions'
A statement read on behalf of Mohamed Al Fayed said the verdicts would come as a blow to "millions" of his supporters around the world.
It continued: "For 10 years I have endured two police investigations. The French and the Scotland Yard inquiries were wrong. These inquests prove it. They said it was an accident and their findings are now dismissed."
As he emerged from the court, he said: "The most important thing is it is murder."
Asked if there would be a court challenge to the verdict by means of a High Court judicial review, Mr Al Fayed's press agent Michael Cole said: "That is a very difficult route but we are keeping all our options open."
The Ministry of Justice confirmed it was not possible for the Crown Prosecution Service to prosecute foreign nationals for deaths abroad, even if the victim is British. All of the paparazzi involved were foreign.
Princess Diana's sister, Lady Sarah McCorquodale, left the court without commenting. A spokesman for the princess's brother Earl Spencer said he would not be making a statement.
Her friend Rosa Monckton told the BBC the inquest had been "incredibly intrusive", adding: "I think there's a lot of her life that has come into the public eye that should never have been there. That's been a very unfortunate side-effect of this inquest."
Speaking about Mr Al Fayed, she said: "One must never forget that he lost a son. I just hope now that he will find some sort of peace."
Former Metropolitan Police commissioner Lord Stevens welcomed the verdicts as a "justification" of the inquiry he led into the deaths.
HAVE YOUR SAY
I hope for the sake of her family, this can finally be laid to rest
He said: "I just hope that this can bring closure to what has been a traumatic event for many people.
"Mr Al Fayed said that he will accept the verdict of the jury. The verdict has been clear. They have said they are absolutely sure that there is no conspiracy in relation to this matter.
"I do hope everybody will take this verdict as being closure to this particular tragic incident and the people who've died will be allowed to rest in peace."
Earlier, Coroner Lord Justice Scott Baker thanked the jury for their "considerable devotion" to duty.