The men, Nicolas Redouane, 49, and Antoine Quirin, 40, had denied raping 39-year-old Emily Spanton, saying the sex was consensual.
But the court was “convinced by the victim's steadfast statements” that she was raped and “by scientific and technical” evidence, its president Stephane Duchemin said on Thursday.
The officers were also ordered to pay 20,000 euros ($23,000) in damages to the victim.
Spanton met the officers on the night of April 22, 2014, at a bar near the fabled police headquarters at 36 Quai des Orfevres, which features in Georges Simenon's Maigret detective novels.
Emily Spanton speaking out about the rape for the first time in 2017. Photo: AFP
She then agreed to visit their offices at “the 36”, where both men were members of the elite BRI anti-gang unit.
The officers, aged 40 and 49, had faced up to 20 years' imprisonment for gang rape.
Prosecutor Philippe Courroye on Wednesday had asked for seven-year prison terms for the officers, who had retained jobs in the police force while awaiting trial.
Spanton was “easy prey”, Courroye said.
That night, he charged, the officers “were not policemen, but usurpers unworthy of their badges, acting in the same way as those they pursue”.
Spanton said she was raped by up to three men but although the DNA of three people was found, only two could be identified.
She told the court that she had been excited to see the “36” and thought “there would be plenty of lights and people”.
But in the middle of the night, their fifth-floor offices were empty.
“I just gave up; just wanted it to be over,” she said.
A view of the police headquarters from across the River Seine. Photo: AFP
Spanton told police officers on duty as she left the building that she had been raped, but said she was treated like a drunk and told to “go home”.
Witnesses described her as looking happy when she entered police headquarters, but distraught when she left.
The trial highlighted flaws in the investigation just after the incident, including that the alleged crime scene was not cordoned off and the officers were allowed to return home without submitting to a breathalyser test.
Spanton's lawyer Sophie Obadia called it “a just decision”, saying the court saw that “Emily Spanton didn't lie”.
As for Spanton, who refused to speak to journalists, she “is very moved and relieved,” said Obadia.
'I am not a rapist'
Both defendants sobbed as they gave their final statements Thursday morning.
“I realise that as a police officer I should never have brought Emily Spanton to the BRI offices,” Redouane said, taking the stand just a few metres away from his accuser.
“All my life I've had good relationships with women. I never, never, never assaulted, attacked or raped Emily Spanton.”
Emily Spanton's lawyer. Photo: AFP
Quirin said it had been a “five-year nightmare” for him and his family.
“Maybe I was unfaithful, but I have never raped a woman. I never raped this woman.”
Quirin's lawyer Anne-Laure Compoint had argued it was not possible to prove beyond doubt that there had been a lack of consent.
Compoint denounced the verdict as “a judicial error”, adding that on appeal “we will refight this case in an atmosphere a lot more calm, and I hope a lot more honest,” she said.
The “36” is still used as police offices, but the headquarters have been moved to a new building in northwest Paris.