The Russian-made MI-17 aircraft was carrying six passengers and four crew when it came down, according to a military statement.
"For us, it is very painful to confirm at this time that the 10 occupants of the aircraft have died," Army commander General Ricardo Gomez said on Twitter.
The authorities had earlier put the toll at seven dead and three missing, but confirmed after rescuers reached the scene that all aboard had perished.
"Our troops are in the area carrying out work to recover the crew and passengers, and investigators have begun to determine the cause" Defense Minister Luis Carlos Villegas said on social media.
President Juan Manuel Santos said he was pained by the deaths as he sent his condolences to the families in a message on his Twitter account.Authorities gave no cause for the crash.
The helicopter was overflying a region used by narcotraffickers and National Liberation Army (ELN) rebels, though there were no suggestions the crash had been caused deliberately.
Santos has suspended peace talks with the ELN in response to what he said were recent guerrilla attacks.
Talks had been set to resume in neighboring Ecuador, but a more than three-month ceasefire expired without immediate agreement to extend it.
"Most likely it was due to bad weather," a military official told AFP on condition of anonymity, saying the weather was squally and cloudy at the time.
The army said two of the passengers were part of a military aviation fuel maintenance team flying between Caucasia and Segovia in the northern Antioquia department.
In October, 10 people aboard a US-made Huey II helicopter were injured when it came down in Bello, Antioquia.
In June 2016, another military helicopter crash killed 17 soldiers in an accident in central Colombia attributed to bad weather. Source from Vietnamnews.