A daring military operation ended the French-Colombian politician's six-year ordeal as a high-profile bargaining chip and dealt a devastating blow to the Revolutionary Armed Forces of Colombia (Farc).

Without a shot being fired military spies tricked the Marxist rebels into handing over their most valuable captives to military helicopters flown by pilots posing as aid workers.

"Thank you for your impeccable operation," a thin but radiant Betancourt told military commanders after being flown to the capital, Bogota. "The operation was perfect."

Composed and eloquent despite the day's emotions and drama, the former presidential candidate added another twist when she said she still hoped "to serve Colombia as president".

Dressed in a camouflage jacket and hat, the 46-year-old stepped off an air force plane into the arms of her mother, Yolanda Pulecio, who had waged a tireless campaign for her freedom.

They embraced and gazed at each other amid applause from military officers, family and friends. Pale but apparently healthy, Betancourt removed her hat to reveal intricately braided dark hair, with plaits and a white flower framing a beaming face. She thanked the Colombian and French governments and expressed hope for peace in Colombia.

Relatives expressed amazement that the gaunt figure glimpsed in harrowing videos had returned. "It is the most beautiful news of my life," said her teenage son, Lorenzo Delloye-Betancourt.

The elaborate military sting "will go into history for its audacity and effectiveness", said the defence minister, Juan Manuel Santos.

"We wanted to have it happen as it did today," said General Freddy Padilla, the head of the armed forces. "Without a single shot. Without anyone wounded. Absolutely safe and sound, without a scratch."

Analysts said the breakthrough could signal the demise of Farc. "For the Farc this is a mortal blow. They will never be able to recover from this," said Alfredo Rangel, director of the Security and Democracy Foundation in Bogotá.

The US president George Bush phoned Colombia's president, Álvaro Uribe, an ally whose security forces are funded by Washington, to congratulate him.

Nicolas Sarkozy, the French president, who had made Betancourt's liberty a priority, also spoke to Uribe and dispatched his foreign minister, Bernard Kouchner, to Bogota.

According to Santos the 15 hostages, who included three US defence contractors and 11 Colombian soldiers and police, were freed in southwestern Guaviare province after intelligence agents infiltrated the guerrillas' leadership and led the commander in charge of the hostages, Cesar, to think they were to be taken by helicopter to Alfonso Cano, the Farc's supreme leader.

The hostages, who had been divided in three groups, were taken to a meeting point where two helicopters piloted by Colombian military agents were waiting. The helicopters took off with the hostages, Cesar and one other rebel, and those two "were neutralised" during the flight, Santos said.

When told that they were free, and not in fact on their way to another Farc camp, the hostages were ecstatic, said Betancourt. "The helicopter almost fell from the sky because we were jumping up and down, yelling, crying, hugging one another. We couldn't believe it," she said.

The government estimates Farc still holds about 700 hostages, many of whom have languished for years in grim conditions.

Betancourt, an outspoken politician, was abducted in February 2002 as she was running for president as an outsider. She became a symbol of the hostages' plight. Images of her face adorned vigils and marches around the world.

As punishment for repeated escape attempts the mother-of-two was tied and chained up and became sick.

The last images of her in captivity showed a frail, despondent woman with lank hair and a blank gaze.

"In all these years, I thought that as long as I was alive, as long as I continued to breathe, I must continue to hope," she wrote in a letter released at the end of 2007. "I don't have the strength I used to have."

Yesterday's news caught her family by surprise. "I am filled with happiness," Betancourt's sister, Astrid, told Colombian radio. "These have been long years of waiting."

Clara Rojas, a political ally who was kidnapped along with Betancourt and freed in January, called the rescue "a blessing from God. I think that meeting again with her children is going to be fundamental for her."

The three American captives, Marc Gonsalves, Keith Stansell and Thomas Howes, were US defence department contract workers who fell into rebel hands in 2003 after their light aircraft crashed in the jungle during a counternarcotics operation.