Miss Knox, 24, and Mr Sollecito, 27, had spent 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."
They have previously spoken of their distress that Miss Kercher had been "nearly forgotten" in the publicity surrounding Miss Knox's appeal and are expected to give a press conference later.
The BBC's Luisa Baldini, who is in Perugia, said the Knox family were seen at an airport in Rome on Tuesday morning and are understood to be flying home to Seattle shortly on a commercial flight.
An eight-member jury cleared both defendants of Miss Kercher's murder after doubts were raised over procedures used to gather DNA evidence.
The judge upheld Miss Knox's conviction for slander for accusing bar owner Patrick Diya Lumumba of carrying out the killing. But he set the sentence at three years, time that Miss Knox has already served, meaning she was free to leave.
She was ordered to pay him 22,000 euros (£18,800) in compensation.
Her family said she had "suffered for four years for a crime she did not commit".
'Nightmare over' 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".
At the sceneAmanda Knox collapsed in tears, hugging her lawyers, as the verdict was read out. Her supporters and those of Raffaele Sollecito cheered at the back of court.
It's been a long battle against lawyers, public opinion and lurid headlines to clear their names. Four years ago, in the days after Meredith Kercher's body was found, it was their erratic behaviour and changing alibis that caught the attention of Perugia's authorities.
Their supporters maintain investigators jumped to conclusions, becoming obsessed with proving their guilt rather than conducting an open-minded investigation.
In this haste, the appeal court heard, mistakes were made - not least in DNA testing. Independent experts dismissed procedures used as well below international standards. Defence lawyers also dismissed the portrayal of Amanda Knox as a danger-seeking, sex-crazed, party girl.
Prosecutors are considering an appeal. Meanwhile, 24-year-old Amanda Knox is expected to make a swift return to the US, where it's understood she'll publish a book about her story.
Mr Sollecito's father Francesco said he had "allowed himself some tears" following the verdict and said the court had "given me back my son".
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.
During the appeal hearing Miss Knox, who was serving 26 years in jail for the killing, had told a packed courtroom: "I did not kill, I did not rape, I did not steal. I was not there."
Tearful, and speaking in fluent Italian, 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".
Miss Kercher had been sharing a cottage in Perugia with Miss Knox, who is originally from Seattle, during a year studying abroad when she was murdered.
Contamination fear 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.
But an independent review disputed those findings, raising concerns over poor procedures in evidence collection and forensic testing, and possible contamination.
It put in doubt the attribution of the DNA traces - collected from the crime scene 46 days after the murder.
In a separate earlier trial, a third person - Rudy Guede, 24 - was convicted of Miss Kercher's murder and was sentenced to 30 years in prison.
His conviction was upheld on appeal but his sentence reduced to 16 years.