American Keith Stansell nears the camera.
"I love my family," Stansell, one of three Americans freed in the operation, tells the cameraman in a big jungle clearing. "Pray a lot."
The local commander, alias Cesar, is put on camera but cheerfully refuses an interview. A Colombian hostage talks to the camera.
The video was shot by Colombian soldiers posing as a media crew during Wednesday's operation, in which the military tricked rebels into giving up the hostages.
The final images in the three-minute video show the hostages as they realize what's up - that after years in jungle prisons, they are finally free.
The moment in which Cesar and the other rebel who accompanied the hostages are overpowered was not captured on video. But the hostages' elation at being freed - many after a decade in captivity - was recorded.
Betancourt, the former presidential candidate kidnapped in 2002, joyfully amazed and crying, hugs William Perez, an army corporal and fellow hostage whom she later credited for nursing her through her jungle illnesses.
Defense Minister Juan Manuel Santos said that among the military intelligence agents making up the helicopter crew - presented as members of an unnamed international humanitarian group - were a nurse, a doctor and agents posing as an Italian, an Australian, an Arab and a Caribbean.
A beacon and microphones also were aboard the Russian-made Mi-17 chopper, allowing those overseeing the rescue to monitor its progress, a U.S. official told The Associated Press, speaking on condition of anonymity because of the subject's sensitivity.
Similar white helicopters carrying International Red Cross personnel and Venezuelan camera crews picked up six FARC hostages in January and February in previous releases brokered by Venezuelan President Hugo Chavez.
Santos denied reports in international media that Israel was involved in the operation, adding that it was "100 percent Colombian."
"Not a single foreigner participated," he said.
He also denied a Swiss radio report that millions of dollars were paid to rebels as ransom in exchange for the hostages.
"If we were to have paid in this instance, we would be the first to acknowledge it," Santos said.
The government pays rewards for information leading to the arrest of FARC leaders. Colombia's government has a US$100 million reward fund from which it has already paid more than US$5 million, officials say.
U.S. authorities were told 10 days before the operation as part of an agreement President Alvaro Uribe made with U.S. President George W. Bush not to take any action without Washington's concurrence, Santos said.
