The FARC was tricked into handing over the hostages by military agents pretending to be Italian, Australian and Arab members of a fictitious non-governmental group who would ferry the captives to the guerrillas' leader.
Trained for weeks by actors, they persuaded the two rebels who boarded the helicopter to leave behind their weapons.
In the air, they subdued the guerrillas - one was left with a large purple bruise across his cheek and nose - and they announced to the hostages their captivity was over.
"We waited and waited years for this," a freed Colombian soldier yelled into the camera.
The Colombian government used the video to showcase its operation and denied reports other nations took part or that it paid a ransom for the freedom of the captives.
Defence Minister Manuel Santos said the military studied films of hostage releases to determine how far the rebels could be pushed into going along with the deception. The idea of binding the 15 hostages came from the rescuers to build credibility with the guerrillas.
JOY IN FRANCE
Betancourt lived in France in her youth and has dual nationality after a now-annulled marriage. After she was kidnapped, the French embraced her as one of their own, staging countless marches and demonstrations on her behalf for six years.
On Friday, dozens of her anonymous supporters cheered and wept at a reception for Betancourt at the presidential Elysee palace, where she hugged and kissed them as Sarkozy beamed.
He had actively sought her release since he took office last year, pressing for negotiations with her captors and urging the Colombian authorities to avoid military action.
The French government was consequently kept in the dark about the Colombian rescue mission, unlike the United States which knew of the plan at least days before and provided signalling equipment. Sarkozy was informed Betancourt had been freed only after soldiers extracted her from the jungle.
Sarkozy's rival in the 2007 election, Socialist Segolene Royal, was swift to jump on this, calling his efforts "useless." She was widely criticized for sounding a negative note.
"(Uribe) wasn't always in favour of all the French initiatives," Foreign Minister Bernard Kouchner said on RTL radio. "This is a victory for him without any doubt, but it is not a defeat for others."
