The helicopters crashed and burst into flame shortly after taking off Monday afternoon near the remote settlement of Villa Castelli in the Andean foothills in northwest Argentina.
Officials said all aboard — eight French nationals and two Argentine pilots — were killed.
Among them were Olympic champion swimmer Camille Muffat, Olympic bronze-medallist boxer Alexis Vastine, and pioneering sailor Florence Arthaud. They had been among the contestants in the reality TV show "Dropped," which was being shot in the sparsely populated region.
Expressions of grief poured in from French athletes and officials, including President Francois Holland, who said he felt "immense sadness." The International Olympic Committee announced it would fly its flag at half-staff for three days.
The bodies were being transported to the regional capital of La Rioja province, where autopsies would be conducted, Judge Virginia Illanes Bordon told The Associated Press.
La Rioja Aviation Director Daniel Gorkich told the AP that both pilots were highly trained and speculated that afternoon sun and strong winds might have been a factor in the crash.
At the moment of impact "the sun was setting on the Andes mountain range directly in front of them," said Gorkich. "Also this is an area with wind gusts."
He said that what happened was "incomprehensible."
The two Eurocopters came down about 50 feet (15 metres) apart and were completely destroyed. One of the aircraft was so charred that only the blades were recognizable.
French officials said they would work with Argentine investigators to determine the cause of the accident, and the Paris prosecutor's office opened an investigation into possible involuntary manslaughter.
The other victims were identified as Laurent Sbasnik, Lucie Mei-Dalby, Volodia Guinard, Brice Guilbert and Edouard Gilles, as well as pilots Juan Carlos Castillo and Roberto Abate.
The wife of Castillo, Cristina Alvarez, told television station Todo Noticias that her husband was a veteran of the Falklands War and had vast experience flying helicopters, including in places like Antarctica.
Her voice cracking, she said her husband was "extremely happy" because he had recently found out he was going to be a grandfather.
La Rioja's regional secretary of security, Cesar Angulo, said one of the helicopters belonged to the government of La Rioja province and the other to neighbouring Santiago del Estero province.
A widely circulated video purportedly shot at the scene shows the blades of one helicopter hitting the rails of the second, causing both aircraft to lose control and crash.
Luis Solorza, press secretary for La Rioja province, told the AP he didn't know who shot the video but that authorities believed it was authentic and investigators were using it as part of their probe.
Solorza said La Rioja's rents out its lone helicopter for events such as the reality show to bring in revenue.
"To promote tourism, we lend out the helicopter," said Solorza, adding that the province had declared two days of mourning.
The crew had arrived Sunday in Villa Castelli, where it had previously filmed a version of "Dropped" for Switzerland and Denmark, said Mayor Andres Navarrete.
Muffat, 25, won gold in the 400-meter freestyle in London, plus a silver medal in the 200-meter freestyle and a bronze in the 4 by 200-meter freestyle relay.
Vastine, 28, won a bronze medal at the 2008 Olympic Games in Beijing and lost in the quarterfinals four years later in London.
But perhaps the best known was Arthaud, 57, a pioneer in sailing. In 1990, she became the first woman to win the famed Route du Rhum race, a trans-Atlantic single-handed yacht race between Brittany and the Caribbean island of Guadeloupe.
The crash was one the deadliest incidents yet related to reality TV shows, some of which involve taking celebrities and others to far-flung places to face challenges both physical and mental.
"Dropped" was being carried by TF1 — France's leading private-sector network — which cancelled another reality show two years ago after a 25-year-old participant died of a heart attack on the first day of filming in Cambodia.
The Adventure Line Productions company was behind both programs. In a statement, it said its staffers were "devastated" and "share the deep pain of the families and loved ones."
Reality TV shows can appeal to former adrenaline-powered star athletes who are looking for new challenges or fun.
William Forgues, Muffat's companion, told i-Tele cable news channel that she was instructed not to reveal details about the show filming, but "told everybody that it was great. She was not forced (to do things). She was where she wanted to be."
"C'est la vie," he added.
Associated Press reporters Peter Prengaman, Victor Caivano and Almudena Calatrava contributed from Buenos Aires. Jamey Keaton and Jerome Pugmire reported from Paris.