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.

On its Twitter feed, the firm reported a second outage this afternoon - which was restored less than an hour later.
"Internet of North Korea down again at 15.41 UTC. Second blackout since last night's restoration of service," the tweet read.
The first outage saw large parts of the internet unavailable in North Korea.
Officials have not yet commented on the issue.
Speculation is rife about the source of the blackouts, following a cyber security row with the US.
China has denounced reports suggesting it was responsible. US officials have not commented on any possible American involvement.
The US had said it would launch a proportional response to the hacking of Sony Pictures, after an FBI investigation appeared to show that North Korea was behind the hack attack which led to films and private emails being leaked online.
The Interview, which depicts the assassination of North Korean leader Kim Jong-un, was cancelled by Sony following threats from hackers.
Internet services in North Korea were down for around nine and a half hours in the first outage, according to Dyn Research.
Some questioned how much an outage would affect a country where normal citizens have little access to the web.
Although many have computers and smartphones, they only have access to a government-approved intranet. Access to the world wide web is reserved for a trusted elite in North Korean society.
North Korea's internet is handled by state-run company Star Join Ventures which is routed through Chinese telecommunications firm China Unicom.
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.
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North Korea appears to have suffered a second internet blackout, according to internet performance measuring firm Dyn Research.