She was seized while campaigning for the Colombian presidency in 2002.
Speaking at a press conference in Paris alongside Betancourt's sister and children, Nicolas Sarkozy, the French president, said that Betancourt was in good health and that her family would fly to Colombia to be reunited with her, along with Bernard Kouchner, the French foreign minister.
In an emotional speech, her daughter Melanie Delloye-Betancourt thanked the French president and Colombian authorities for the "long awaited" moment.
Al Jazeera's Monica Villamizar in the Colombian city of Cartagena says the hostages are currently being flown by helicopter to a military base near the Colombian capital, Bogota, where they will receive medical treatment.
The government has also said the former hostages are to be shown on Colombian television, our correspondent adds.
|Three US Pentagon contractors were
seized in 2003 [EPA]
Friends and family of Betancourt 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 chained to a table and looking gaunt and frail.
The three US hostages are contractors for the US Pentagon who were seized by the Farc after their plane went down in Colombia in 2003.
Images of Keith Stansell, Thomas Howes and Marc Gonsalves were also released last November, showing the men in relatively good health.
Earlier this month Alvaro Uribe, Colombia's president, said a member of the Farc had offered to release Betancourt.
The group, which has been fighting the Colombian government for more than 40 years, also holds around 30 other foreign hostages and is also thought to be holding hundreds of Colombians in captivity.
|The Farc was hit by the death of leader
Marulanda in May [AFP
In May, Bernard Kouchner, the French foreign minister, travelled to Colombia for talks with Uribe over securing her release.
The country had sent a mission to Colombia in April in a bid to provide the reportedly ailing politician with medical treatment, however the Farc said it had not been consulted over the mission.
The Farc has released six hostages this year following mediation efforts by Hugo Chavez, the Venezuelan president, and has 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 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.