The two were met by members of the International Committee of the Red Cross under whose auspices the operation was undertaken by the Colombian and Venezuelan governments.
It is the first time Farc, Latin America's oldest rebel group, has released any of its high-profile hostages.
'Being reborn'
Hugo Chavez, the Venezuelan president who will meet the two women in Caracas, had earlier announced that the helicopters he sent into Colombia had picked up the two former politicians and he had spoken to them by telephone.
"They are free. I told them both, 'Welcome to life,'" he told reporters.
"It still seems like I'm kind of dreaming," Rojas' mother Clara de Rojas, said in Caracas, her voice choked with tears.
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Chavez says more hostages could
now be released [AFP] |
"President [Chavez], a thousand thanks for your humanitarian gesture," Gonzalez, a former congresswoman was shown telling told Chavez on a satellite phone.
"We are being reborn," Rojas told Chavez.
Chavez said he hopes the mission opens the way for the release of more hostages.
Farc is holding about 46 high-profile hostages hoping to exchange them for hundreds of its jailed fighters.
Mariana Sanchez, Al Jazeera's correspondent in Caracas, said the two women appeared far healthier than anyone could have expected given previous images of the former Colombian presidential candidate Ingrid Betancourt, looking gaunt.
Betancourt's family welcomed the release of Rojas, a former aide to the French-Colombian politician who remains in captivity.
'Progress is possible'
"I am deeply moved. This is a wonderful step towards bringing home all the other hostages, including my mother," Melanie Delloye, Betancourt's daughter said.
"It shows that when there is a will, progress is possible."
The release of Rojas, who was abducted in 2001, and Gonzalez, who was taken in 2002, is a boost for Chavez who had seen his relations sour with his Colombian counterpart, Alvaro Uribe, after a similar rescue deal collapsed last month.
On Thursday a laboratory in Spain confirmed DNA results showing that a three-year-old boy at a Bogota orphanage is the son of Rojas, born in captivity.
Chavez promised last year he would secure the release of the two women and the boy, Emmanuel, but the deal collapsed as it emerged the boy had already been in the hands of Colombian officials for more than two years.
Monica Villamizar, Al Jazeera's correspondent in Bogota, said the whole of Colombia was tuned in to the story and that there would now be hopes of more hostage releases.
Villamizar said relatives of other hostages are waiting anxiously for news and although there were unconfirmed rumours that more captives could be handed over, families were hoping at least for proof of life through letters or other documents brought by Rojas and Gonzalez.