Ingrid Betancourt, the French-Colombian politician held hostage by Farc rebels for more than six years, has thanked the Colombian army for rescuing her.
Television images from a military base near the Colombian capital, Bogota, showed Betancourt, who appeared to be in good health, embracing her mother and husband after landing at the base.
"Thanks to all Colombians and those worldwide who made it such that we are alive," she said at a news conference.
Three US hostages and 11 Colombian soldiers were also freed on Wednesday in a "special intelligence operation", Juan Manuel Santos, the Colombian defence minister, said.
An aeroplane carrying the three Americans touched down at a US air force base in San Antonio, Texas early on Thursday.
George Bush, the US president, and Nicolas Sarkozy, the French leader, called their Colombian counterpart Alvaro Uribe to congratulate him.
Analysts say the operation's success strengthens Uribe's already high popularity in Colombia and puts further pressure on the Revolutionary Armed Forces of Colombia (Farc) group, which had already weakened by the loss of key leaders and desertions.
"God, this is a miracle, such a perfect operation is unprecedented"
rescued Farc hostage
Betancourt, the group's most high profile hostage, had been held by the Farc in remote jungle territory near the city of San Jose del Guaviare.
She and the others were flown from the region to the Catam military base for medical treatment following the operation to free them.
At a news conference, Betancourt described her years in captivity and the operation to release her, praising the Colombian and French leaders as well as the Colombian army, often crying as she spoke.
"God, this is a miracle, such a perfect operation is unprecedented," she said.
Speaking in Paris earlier on Wednesday, alongside Betancourt's sister and children, Sarkozy said that Betancourt's family would fly to Colombia along with Bernard Kouchner, the French foreign minister, to be reunited with her.
In an emotional speech, her daughter Melanie Delloye-Betancourt thanked the French president and Colombian authorities for the "long awaited" moment.
The three US former hostages are contractors for the US Pentagon who were seized by the Farc after their aircraft went down in Colombia in 2003.
Keith Stansell, Thomas Howes and Marc Gonsalves were already on their way to the US, Colombia's government said.
'You are free'
Santos, the defence minister, said the operation began when Colombian military spies infiltrated the Farc group and tricked the rebel commander holding the hostages into thinking the hostages were to be taken to Alfonso Cano, the group's top leader.
|The three US Pentagon contractors were
seized in 2003 [EPA]
Betancourt later said at the press conference following her release that the hostages, who had been divided into three groups, were taken to a rallying point on Wednesday morning where two disguised helicopters piloted by Colombian military agents were waiting.
It was not until the helicopters were airborne, Betancourt said, that the mission's commander turned to her and said: "We are the national army, you are free."
Santos also said that two rebels on the aircraft were detained but that no Farc rebels on the ground were hurt during the operation and they were permitted to escape "in hopes that they will free the rest of the hostages" - thought to number a total of 700, including around 40 foreign hostages.
"[The operation] will go into history for its audacity and effectiveness," the defence minister said, but added that the government was willing to negotiate with the rebel group.
"The government reiterates to them that if they want to enter into serious negotiations in good faith, we are offering a dignified peace," he said.
|The Farc was hit by the death of leader
Marulanda in May [AFP]
Friends and family of Betancourt, who was seized while campaigning for the Colombian presidency in 2002, had campaigned for years to secure her freedom.
Betancourt's health had reportedly been failing in recent months and her family had said she was severely depressed, close to death and in urgent need of medical treatment.
A series of images and video released last November of Betancourt showed her chained to a table and looking gaunt and frail.
The Farc released six hostages this year following mediation efforts by Hugo Chavez, the Venezuelan president, and had indicated a willingness to exchange others for Farc prisoners in Colombian jails.
One of those released was Clara Rojas, Betancourt's former aide, who spent six years alongside Betancourt in captivity.
The group, which has been fighting the Colombian government for more than 40 years, is thought to have been weakened by desertions and the killing of two of its senior leaders, and in May it said that its top commander, Manuel Marulanda, had died of a heart attack.