A pale Ms Betancourt smiled as she emerged with other hostages from a military plane in the Colombian capital, Bogota, to be greeted by her mother and husband.
She appealed to Farc to free the other hostages and make peace.
She thanked Mr Uribe, against whom she was running as a presidential candidate when she was kidnapped, and said he "has been a very good president".
"I continue to aspire to serve Colombia as president," she said.
French President Nicolas Sarkozy, who had made the rescue of Ms Betancourt a foreign policy priority, was joined by her family at his residence, the Elysee Palace in Paris.
The freed hostage's son, Lorenzo Delloye-Betancourt, told the news conference it was "the best moment of my life". His sister Melanie said it was like "emerging from a bad dream".
The siblings are flying to Colombia to be reunited with their 46-year-old mother.
Video pictures released last November had shown Ms Betancourt looking gaunt and frail.
Accounts from freed hostages that she was in danger of dying had heightened the sense of urgency surrounding her fate.
Naked and blindfolded
Also released were three US defence department contract workers who were captured after their light aircraft crashed in the Colombian jungle in 2003.
The trio - Marc Gonsalves, Thomas Howes and Keith Stansell - have now arrived back in San Antonio, Texas, where they will undergo medical tests and be reunited with their families.
Ingrid Betancourt's son on his joy at her release
The 11 members of the Colombian security forces who were released had been captured in various rebel attacks.
Colombian Defence Minister Juan Manuel Santos said the Farc rebels had been tricked into handing over the hostages by soldiers posing as members of a fictitious non-government organisation that supposedly would fly the captives to a camp to meet rebel leader Alfonso Cano.
"The helicopters, which in reality were from the army, picked up the hostages in Guaviare and flew them to freedom," he said.
Intelligence agents had infiltrated the guerrilla ranks and duped the local commander in charge of the hostages, alias Cesar, the defence minister said.
Cesar and another rebel who boarded the helicopter had been quickly overpowered and would now face justice, he added.
'Without a scratch'
Ms Betancourt later told a press conference she at first had had no idea she was being rescued until she saw her captor naked and blindfolded on the floor of the aircraft.
STEPPING STONES TO FREEDOM
Jan, 2008: Betancourt aide Clara Rojas and ex-congresswoman Consuelo Gonzalez freed by Farc
Feb, 2008: Farc vows to hold three US hostages for 60 years
March, 2008: Colombian forces raid rebel camp in Ecuador and kill Farc commander Raul Reyes
March, 2008: Farc leader Manuel Marulanda dies of reported heart attack
April, 2008: Farc says Ecuador raid has "gravely" harmed efforts to free Ms Betancourt
July, 2008: Colombian military frees Ms Betancourt, the three US contractors and 11 other hostages
"I saw this guerrilla commander, who had so often been cruel to us, on the floor," she said. "But I did not feel happiness. I felt sad."
Armed forces chief Gen Freddy Padilla said: "We wanted to have it happen as it did today. Without a single shot. Without anyone wounded. Absolutely safe and sound, without a scratch."
The US ambassador to Colombia, William Brownfield, said there had been "close co-operation" from the Americans, including sharing of intelligence, equipment and training advice.
World leaders welcomed the news, and celebrations erupted on the streets of Colombian cities as crowds hailed the jungle rescue in a country plagued for decades by kidnappings.
The BBC's Jeremy McDermott in Medellin says the successful operation by Colombian security forces is a political and military coup for the country's government.
The released American hostages have flown home
He adds that it is a major blow to the Farc, which had hoped to exchange some 60 political hostages for hundreds of rebels held by the Colombian government, and has now lost a powerful negotiating tool with Ms Betancourt's rescue.
The Farc still holds more than 40 high-profile hostages, among up to 700 other captives.
Ms Betancourt has dual citizenship as the result of marriage to a French diplomat - since dissolved - which produced her two children, who worked hard to keep her captivity in the spotlight.
The politician was kidnapped in February 2002 while campaigning in territory controlled by the Farc.
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