Intelligence operatives had also infiltrated the cell of rebels led by Gerardo Aguilar Ramirez, the man known as "Cesar", who were holding the 15 hostages.
FROM THE TODAY PROGRAMME
Three of those freed on Wednesday were US defence department contractors, and Operation Check - as in "checkmate" - came after months of preparation and co-operation with US security services.
Gen Padilla told the Associated Press that a disgruntled member of Farc, trusted by the rebels' high command, had agreed to spearhead the operation.
He convinced Cesar that commanders wanted the 15 hostages moved to a rallying point in southern Colombia, the general said, adding: "The Farc's communications are medieval."
Cesar believed that the hostages were to be delivered by helicopter to another Farc leader, Alfonso Cano, at a location somewhere between La Paz and Tomachipan, according to Defence Minister Juan Manuel Santos.
A day before the operation, two helicopters - painted white and disguised as those of a fictitious non-governmental organisation - left a military base in an Andean mountain valley and settled in a wilderness clearing.
Juan Carlos Bermeo
Jose Ricardo Marulanda
Jose Miguel Arteaga
On board one of the helicopters - the one that would rescue the hostages - were four air force crew disguised as civilians, seven military intelligence agents and the rebel turncoat, military officials said.
Two of the agents had dressed as rebels, and the rest wore white as though they were members of a humanitarian mission. All had taken a week and a half of acting lessons, Gen Padilla said.
When the helicopters arrived at the rendezvous point at midday on Wednesday, one touched down while the other hovered in case of an emergency, sources told the Colombian news website Semana.com.
Gen Padilla said the crew instructed the rebels to bind the hostages' hands because 14 of them had military training.
"Nobody wanted to risk them trying to overpower the crew," he told AP.
Once the aircraft was airborne, the rescuers - some wearing T-shirts bearing the portrait of legendary revolutionary Ernesto "Che" Guevara - swiftly overpowered Cesar and his aide.
The rebels were disarmed, stripped naked and tied up as the liberated hostages celebrated so jubilantly that, in the words of Ms Betancourt, "the helicopter nearly fell from the sky".
If things had gone wrong, the Colombian military had a Plan B for 39 helicopters and 2,000 troops to encircle the hostage-holders and try to persuade them to surrender peacefully.
The general said the turncoat was now free and likely to receive a sizable reward.
William Brownfield, the US ambassador to Colombia, confirmed that Washington and Bogota shared intelligence, equipment, training advice and operational experience prior to the complex operation.
Hailing the rescue mission's success, Colombian President Alvaro Uribe said: "It was an intelligence operation comparable with the greatest epics of human history, but without a drop of blood being spilled, without one weapon being fired."
HOW RESCUE OPERATION UNFOLDED
Around midday two army helicopters painted white arrived at rebel site near Ininda River, a second waited at nearby clearing as back-up.
Undercover soldiers said hostages would be taken to another rebel leader, somewhere between La Paz and Tomachipan.
Once on board helicopters, two rebels were overpowered, 15 hostages freed and Ingrid Betancourt eventually flown to capital Bogota.
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