The inquest has lasted six months
Princess Diana's sons have tried to draw a line under years of speculation surrounding her death with a statement welcoming her inquest verdict.
In a message to jurors, Princes William and Harry said: "We agree with their verdicts and are both hugely grateful."
The inquest found Princess Diana and Dodi Al Fayed were unlawfully killed due to the "gross negligence" of driver Henri Paul and the paparazzi.
But Mr Al Fayed's father Mohamed has refused to accept the verdicts.
The princes thanked the jury "for the forbearance they have shown in accepting such significant disruption to their lives over the past six months".
They also commended coroner Lord Justice Scott Baker for "his unfailing courtesy and for all the consideration shown by him and his staff not only to us but to all those involved in this hearing".
They added: "We are particularly grateful to Trevor Rees and to others who came forward to give evidence - in many cases reawakening their painful and personal memories.
"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."
The jury of six women and five men returned joint verdicts of unlawful killing through grossly negligent driving - or gross negligence manslaughter, by a 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 exceed £10m.
But Mohamed Al Fayed has rejected the verdicts. His spokeswoman Katharine Witty told BBC News 24: "I think he is just going to reflect on the full ramifications of the verdict."
Princes Harry and William have expressed their gratitude to the jurors
Asked if he would challenge it through judicial review, she said: "I think it is something he is considering...I think he is going to be very mindful of what people are saying - which is that it should end here."
She said Mr Al Fayed accepted some issues had "fallen away" during the inquest, but added: "It is possible that MI6 were involved...we are still saying that, it's possible, but whether...we can do anything about that remains to be seen."
'Waste of money'
In a statement issued immediately after the jury's decision, Mr Al Fayed said the verdicts would come as a blow to "millions" of his supporters around the world.
He also insisted the hearing, held largely at his behest, had not been a waste of time or money.
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I hope for the sake of her family, this can finally be laid to rest
This was not the opinion held by many of those who answered a BBC Newsnight poll on the subject.
The survey of 1,000 people found 78% thought the estimated £10m bill had not been well spent and 62% thought the princess's death was a tragic accident.
Despite the verdicts, the Ministry of Justice has confirmed it is 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.
'Playing with fire'
Phil Hall, News of the World editor at the time of the crash, said everyone must take responsibility for the tragedy, including the public which had "a voracious appetite" for photos of the couple.
But Princess Diana was "playing with fire" by courting the press, he told BBC Radio 5 Live, adding: "Where it goes wrong is when you have photographers acting as a mob and a driver who clearly is drunk."
Meanwhile, Princess Diana's former Butler, Paul Burrell, is waiting to discover whether he will be investigated by the police for perjury for allegedly lying at the inquest.
Scotland Yard has so far refused to confirm whether there will be an inquiry, but the Crown Prosecution Service said if the police gave them a file on the matter, they would investigate it.