They said the case, in which the accuser became the accused, should now be reviewed by an independent, foreign police force.
The young woman, who cannot be named for legal reasons, was 19 when she claimed that she was raped by up to a dozen Israeli teenagers and young men in a hotel room in the party town of Ayia Napa in July 2019.
About a week later she retracted the claim and was charged with causing public mischief.
Her lawyers said she only retracted the claim because she came under extreme pressure from Cypriot police – a charge that officers denied.
Mr Polak said the judge had ignored testimony from a British clinical psychologist, who had told the court the young woman was suffering from PTSD, as well as evidence from a forensic linguist, who said it was likely that Cypriot police had coached the woman as to what to write in her retraction statement.
Police had failed to collect all the evidence relating to the gang rape and failed to download data from the suspects' mobile phones.
"We believe that the next step for justice to be done in this case is a full review and investigation by a different police force of the rape complaint put forward by our client.
Nicoletta Charalambidou, one of the Cypriot lawyers for the woman, also said the case should be reviewed.
"The acquittal by the Supreme Court ... points to the failure of the authorities to effectively investigate the rape claims she reported. This is what we will now pursue," she said.
Lewis Power, a British QC who was also on the defence team, said: "It is with great joy that we learn that this young woman has at last received the justice she so rightly deserved, that which had been thus far so cruelly and unjustly denied.
"We hope that this decision will have far reaching implications in the pursuit of justice for other victims of sexual assault."
At a trial in the nearby town of Paralimini, she was found guilty in January 2020 of causing public mischief and given a suspended four-month jail sentence.
Her legal team argued that the trial was deeply flawed and the conviction unsafe.
They said that the British woman was interviewed in a police station for more than six hours without a lawyer or translator. They said she was suffering from PTSD as a result of the alleged sexual assault.
The Israeli teenagers and young men denied any wrongdoing and were eventually released from custody and allowed to return home.
"It is with great relief that we hear that the authorities in Cyprus have recognised the flaws in their legal process," said the mother of the Briton, who is now a university student.
"Whilst this decision doesn't excuse the way she was treated by the police or the judge or those in authority, it does bring with it the hope that my daughter's suffering will at least bring positive changes in the way that victims of crime are treated."
The young woman is still suffering from post traumatic stress disorder following her ordeal, her grandfather said.
"This is great news and my grand daughter will be very pleased and relieved. All this has affected her, although she is getting on as best as she can with her life. At times she has still been struggling and affected by PTSD.
"I'm very happy with the news. It's my birthday today and we'll be having a bit of a celebration. We wanted her exonerated and finally she has been."
Michael Polak, from the organisation Justice Abroad, who coordinated the appeal, said: "This is a watershed moment, not just for our client who has always maintained her innocence even when doing so caused her the hardship of not being able to return home during the lengthy trial proceedings, but also for others around the world in similar positions.
"Important fair trial provisions, which are in place to prevent miscarriages of justice, were totally disregarded in this case. A young and vulnerable woman was not only mistreated when she reported the rape to the police but then she was put through a trial process that was manifestly unfair - as the Supreme Court has recognised."
