(CNN) -- In a secret operation a U.S. official called "brilliant," the Colombian military infiltrated rebel group FARC and deceived its members into giving up 15 hostages including former Colombian presidential candidate Ingrid Betancourt, Colombia's defense ministry said.

Appearing healthy after being held hostage for six years in the jungle, Betancourt walked down from a Colombian military jet in Bogota on Wednesday and hugged her mother and husband, a broad smile on her face.

"God carried out this miracle," she said. "This is a miracle because I know that all of you suffered with my family, my children, with me. This is a moment of pride for all of Colombia for such a perfect operation."

Along with Betancourt, three American contractors and 11 other hostages who were Colombian police were rescued in Wednesday's operation.

The 46-year-old Betancourt is a former senator who fought Colombia's drug cartels as a congresswoman in the 1990s. She ran for president in 2002, calling for a nation "free of corruption, violence and free of drugs."

As a hostage, she was reduced to a frail woman whose health was reportedly in serious jeopardy.

She said she awoke Wednesday at 4:30 a.m. and said the rosary, then was told by her guards that she and the other hostages were to be transferred to another location, where their detention was to continue.

"My heart broke because I did not want another transfer, another time, in captivity," she said.

But her guard, a woman, was unmoved, and ordered Betancourt to cross a river to the pickup spot -- "very harsh, move, hurry up fast, as always," she said.

Soon, two white helicopters approached and several men approached the Revolutionary Armed Forces of Colombia commanders who were overseeing their transfer, she said.

"They spoke with Commander Enrique and Cesar," she said of her captors. As she looked closer, she saw that the men from the helicopter were wearing shirts emblazoned with the likeness of Che Guevara, the Argentine hero of the Cuban revolution. "I thought, this is FARC," she said.

Placed in handcuffs, Betancourt got into the helicopter, still unaware of what was happening. "They closed the helicopter doors, the helicopter started flying and suddenly there was something happening," she said.

"Suddenly I saw the commander who, during four years, had been at the head of our team, who so many times was so cruel and humiliated me, and I saw him on the floor naked with bound eyes."

Then, the reality of her liberation hit home.

"The chief of operations said, 'We are the national army and you are all free,' and the helicopter almost fell because we started jumping, we screamed, we cried, we hugged. We couldn't believe it." Watch Betancourt call the operation 'perfect' »

Not a single shot was fired, she added.

Colombian Defense Minister Juan Manuel Santos said the Colombian military infiltrated the FARC leadership and arranged for the hostages to be taken to the south of the country, where they were to be picked up by helicopters that the rebels believed were controlled by another group.

They were initially transported to a military air base southwest of Bogota, from which they were to travel later Wednesday to the capital, a military spokesman said.

She added that she hopes that FARC commanders would not punish the guards who were fooled. It was not their fault, she said; the operation was too perfect for them to detect the deceit.

The FARC, which has fought a longstanding and complicated conflict with Colombia's government and right-wing paramilitary groups, defends the taking of captives as a legitimate act of war and is believed to hold roughly 750 prisoners in the nation's remote jungles.

The freed hostages also include Americans Keith Stansell, Marc Gonsalves and Thomas Howes.

A senior U.S. State Department official told CNN the families of the hostages had no idea the rescue operation was taking place.

The plight of Betancourt, who has French and Colombian citizenship, has attracted worldwide attention.

She was abducted February 23, 2002, after venturing into rebel territory while campaigning for the Colombian presidency. Videos later showed a slim Betancourt, sitting silently in a jungle setting.

News of her deteriorating health came after the FARC released six hostages this year. One of the freed hostages, Luis Eladio Perez, said that Betancourt had suffered from chronic liver problems since 2004.

He said he last saw her February 4 this year.

"Ingrid made a sign for me to go to the bathroom, and she did the same, and we were able to talk for about five minutes," Perez said. "I saw she was very ill and wasting away. She looked much worse than in that 'proof-of-life' video the rebels filmed in October."

Betancourt "seemed desperate," even though "she told me to stay calm and that the guerillas were giving her vitamins and calcium," he said.

French President Nicolas Sarkozy expressed gratitude to Colombian authorities and said Betancourt "is in good health." Watch Sarkozy give thanks »

Betancourt's jubilant daughter, Melanie Delloye, said, "I feel like I've just awakened from a bad dream." Watch family daughter talk about getting mother back »

She and other members of the family spoke alongside Sarkozy.

U.S. President George W. Bush congratulated Colombian President Alvaro Uribe by phone. Uribe is slated to address the nation at 10 p.m. ET (0200 GMT).

A senior State Department official said the United States played no role in the operation, though it was briefed on it ahead of time. The official called the operation "brilliant" and "a huge success," saying it involved a deception operation against the FARC.

According to Pentagon officials, Colombians told the United States about the operation in the past few days. The U.S. approved the plans but had no part in them.

The United States is offering medical support to the three American contractors, including a medical evacuation back to America.

William Bronfield, a senior U.S. ambassador, confirmed the United States was briefed about the operation. He is on his way to the Colombian airbase where the hostages were taken.

Contractors Stansell, Gonsalves and Howes have been held since February 13, 2003, when their single-engine plane crashed in the mountains south of Bogota. The Americans were working for Northrop Grumman Corp. as part of a U.S.-funded counternarcotics effort.

Two other men on the plane, American pilot Tommy Janis and a Colombian, were shot to death by FARC. A rescue plane searching for the men crashed six weeks later, killing its American pilot, Butch Oliver, and another American crew member.

Stansell, Gonsalves and Howes were last seen in a 2003 interview by a Colombian journalist who made his way into a FARC stronghold. The journalist's video was shown on CBS' "60 Minutes."

"To our country, we miss you, and we hope we return one day. We're alive and well," said Stansell, then 38, a systems analyst.

"We expect to get out of here one day. We can't say for sure," said Howes, then 50, a professional pilot. "But our main concern is the welfare of our families."

"I'm a proud American," said Gonsalves, then 31, also a systems analyst. "I look to you guys, and I ask for a diplomatic solution to get us home safe, please."

CNN's Jim Bittermann in Paris contributed to this report.

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