The woman was arrested and had her passport confiscated after she claimed she was raped by two British men.
The Dubai Public Prosecutor's office said it had closed the case after "careful examination of all evidence".
It said investigations showed "the act happened with the consent of the three parties in question".
A video on one of the suspect's mobile phones was found to be "key evidence".
Officials said there would be no legal action and all three parties were in the process of receiving their passports and were free to leave the United Arab Emirates (UAE).
The woman's father said he had received "conflicting stories" saying that his daughter had been released, but he said the Foreign Office had not confirmed anything yet.
The woman, in her 20s, reported the alleged rape at a police station in late October, a statement from the prosecutor's office said.
She was reported to have been holidaying in Dubai.
The two male suspects were also arrested, questioned and had their passports confiscated, but no charges were filed against them.
The campaign group, Detained in Dubai, said it was pleased with the decision.
"We expect that the international outrage that this case deserved, influenced authorities to drop the charges, in order to spare the UAE of such negative press.
"Others in the past have not been so fortunate but we hope that this landmarks a fresh approach to similar cases in the future."
The public prosecutor's office said Dubai's legal system takes reports of all crimes "very seriously, including and especially violence against women, and conducts thorough investigations of all incidents".
In Dubai all sex outside of marriage is illegal. If authorities become aware of a sexual relationship, those involved risk prosecution, imprisonment and/or fine and deportation.
A British woman, who was charged with having extra-marital sex in Dubai after reporting she was raped, has had all charges against her dropped.