"Apparently, the two helicopters collided as they were filming. There are no survivors," provincial spokesman Horacio Alarcon told AFP.
He said the weather conditions were good and the cause of the crash, which happened late afternoon local time on Monday, was unknown.
Local media showed the wreckage of the two helicopters in flames on the dry scrubland in the northwestern Argentinian province.
Eight French passengers and their two Argentine pilots died in the crash, a police source said.
Arthaud, 57, was considered one of the best sailors in the world, a woman who conquered what had been a strictly male dominated sport. Her titles included the 1990 Route du Rhum, the most prestigious race to cross the Atlantic solo.
Muffat, 25, was one of the top swimmers in French history, winning three medals at the London Olympics in 2012, including gold in the 400-metre freestyle.
She shocked the sporting world in June 2014 by announcing her sudden retirement at the age of 24, exhausted by the long hours of training in the pool.
Vastine, 28, won a bronze medal at the Beijing games in 2008 in the light welterweight category.
'Immense sadness'
President Francois Hollande led the tributes, saying the "brutal death of our compatriots is an immense sadness."
"The whole of France is in mourning this morning," said Prime Minister Manuel Valls.
The reality TV show, called "Dropped", involved eight sports stars being dropped into inhospitable environments for an adventure- and survival-themed show.
Fellow contestant, former France and Arsenal football star Sylvain Wiltord, said on Twitter he was "sad" and "horrified."
The other stars participating in the show -- none of them hurt in the accident -- were swimmer Alain Bernard, cyclist Jeannie Longo, snowboarder Anne-Flore Marxer and figure skater Philippe Candeloro.
The other stars participating in the show -- none of them hurt in the accident -- were swimmer Alain Bernard, cyclist Jeannie Longo, snowboarder Anne-Flore Marxer and figure skater Philippe Candeloro.
