Amanda Knox and ex-boyfriend Raffaele Sollecito have been cleared of killing UK student Meredith Kercher following a successful appeal in Perugia, Italy.
Miss Knox, 24, and Mr Sollecito, 27, had been convicted in 2009 of murdering the Leeds University student, 21, from south London, two years earlier.
American Miss Knox sobbed as they were freed after nearly four years in jail.
Miss Kercher's family said they did not understand how the original verdict could be so "radically overturned".
However, the family - in Perugia for the decision - added in a statement: "We still trust the Italian justice system and hope that the truth will eventually emerge."
The judge had upheld Miss Knox's conviction for slander after she accused bar owner Patrick Diya Lumumba of carrying out the killing. He set the sentence at three years, time that Miss Knox has already served.
But the eight-member jury cleared both defendants of Miss Kercher's murder after doubts were raised over procedures used to gather DNA evidence.
Miss Knox is expected to fly back to the US on Tuesday. Her family said she had "suffered for four years for a crime she did not commit".
Speaking on the steps of the court, Miss Knox's sister Deanna said: "We are thankful to the court for having the courage to look for the truth and to overturn this conviction."
She said Miss Knox's "nightmare was over" and asked for privacy for her family to recover from "this horrible ordeal".
Her lawyer, Carlo Della Vedova, said outside court that there was "no winner" in the case and the appeal court had "rectified a mistake".
"Meredith was a friend of Amanda - we should never forget this and we have to respect the sorrow of all the families," he told the BBC.
Mr Sollecito's father Francesco said he had "allowed himself some tears" following the verdict.
"We will remember her with affection," he said of Miss Kercher.
'Years of suffering'
"I would have liked to talk to her relatives as well, as they have lost a daughter in a very cruel way.
"But tonight, they have given me back my son."
Giulia Bongiorno, Mr Sollecito's lawyer, said: "I don't want to stress the four years of suffering that these two young people went through but I do want to stress the extremely positive outcome of this trial."
Hundreds of people had gathered in the streets outside the court ahead of the verdict and some shouted "shame" when they heard about the decision, while others cheered.
Miss Kercher's mother Arline left the court without commenting and was escorted into a waiting car before being driven away. The Kercher family had earlier said they would speak at a news conference the day after the verdict.
Earlier in the day, Miss Knox, who was serving 26 years in jail for the killing, was given a final chance to state her case in a personal statement and she told a packed courtroom she was "paying with her life".
Tearful, and speaking in fluent Italian, the American said: "I did not kill, I did not rape, I did not steal. I was not there."
She added: "I want to go back home. I want to go back to my life. I don't want to be punished. I don't want my life and my future to be taken away for something I didn't do because I am innocent."
Her ex-boyfriend Mr Sollecito, who had been given a 25-year term after the initial trial, told the court in his statement that he was in a "nightmare" and said the claims against him were "totally untrue".
Human rights lawyer Paul Gilbert told the BBC News Channel it would be difficult for Miss Knox to get compensation from the Italian justice system as she would need to show she had been the victim of a "malicious prosecution".
Prosecutors had said beforehand they would appeal if the verdict was overturned, although it appears unlikely that Miss Knox would be extradited back to Italy from the US.
They had called for Miss Knox and Mr Sollecito's sentences to be increased to life in prison.
Miss Kercher had been sharing a cottage in Perugia with Miss Knox, who is originally from Seattle, during a year abroad from Leeds University when she was murdered.
Prosecutors said she was killed in a brutal sex game which went wrong. Her throat had been slit and she had been sexually assaulted.
They maintain that Miss Knox's DNA was on the handle of a kitchen knife - found in Mr Sollecito's flat and believed to be the murder weapon - with Miss Kercher's DNA on the blade.
They also said Mr Sollecito's DNA was on the clasp of Miss Kercher's bra.
But an independent review disputed those findings, raising concerns over poor procedures in evidence collection and forensic testing, and possible contamination.
It placed into doubt the attribution of the DNA traces - collected from the crime scene 46 days after the murder.
A third person - Rudy Guede, 24 - had been convicted of Miss Kercher's murder in a separate trial and was sentenced to 30 years in prison.
His conviction was upheld on appeal but his sentence reduced to 16 years.