There are five confirmed survivors, Alfredo Bocanegra, the head of the civil aviation authority said, including three Chapecoense Real soccer team players, two crew members and one journalist.
One of the dead, survived the crash but died in hospital.
"Six people were rescued alive, but unfortunately one died. The rest of the occupants unfortunately died. The tragic toll is 76 victims," Jose Gerardo Acevedo, regional police commander, told journalists.
Brazilian TV channels Globonews and SporTV identified the surviving players as defender Alan Ruschel, goalkeeper Danilo and reserve goalkeeper Jakson Follmann.
Four survivors have reportedly been brought to safety, including Ruschel, and a stewardess, who were taken to a hospital in the town of Le Ceja, local authorities said, quoted in Colombian newspaper El Colombiano's online edition.
The flight was carrying 72 passengers and nine crew members, according to authorities. Brazilian news organizations reported 21 journalists had been on board.
Rescue operations at the site were suspended in the early hours of Tuesday morning amid heavy rain, Medellin airport said.
The pilots of the plane were reportedly having problems with the electronics system before the accident, the airport authorities said on their Twitter feed.
The crashed aircraft was a British Aerospace 146 short-haul plane operated by Bolivian charter airline Lamia, authorities said. They said the plane had declared an emergency at 10 p.m. Monday (0300 UTC Tuesday) due to an electrical failure.
"It's a tragedy of huge proportions," Medellin's mayor, Federico Gutierrez, said while traveling to the crash site in a mountainous area outside the Colombian city.
Brazil's Chapecoense football team had been due to play Atletico Nacional for the Copa Sudamerica finals in Medellin on Wednesday.
