Alvaro Uribe, the Colombian presdient, had claimed that the communist revolutionaries could not have kept their promises because they did not have the boy, who had been living in care under a different name, Juan David Gomez.
On Saturday, Farc said the boy was in care only because there were threats by the government to kidnap him and because Farc constantly moves its bases. A source from the attorney general's office gave a different account, saying the boy has been in the home since 2005.
A Farc statement, realeased two hours after the government's announcment on the DNA analysis, said the boy was placed in foster care to protect him from anti-guerrilla operations.
The statement, posted on a website, read: "That's why the boy, of a guerrilla father, was placed in Bogota under the care of honest people, while a humanitarian agreement was being signed."
Judge Mario Iguarán, chief federal prosecutor, said that DNA samples taken from the boy and Clara Rojas's mother, showed a complete match between the mitochondria in the blood, meaning that there is a "very high probability" that "the boy belongs to the Rojas family".
|Grandmother Clara Gonzalez de Rojas, right,|
provided blood for analysis [AFP]
"The scientific proof indicates that the child in the care of the Colombian Family Welfare Institute is Clara Rojas's child," Iguarán said.
"There is a small margin or error, but a second test will be performed in Spain to provide confirmation."
Iguarán added that DNA test results prove the speculation that a child was born of an allegedly consensual relationship between Rojas and one of her captors.
Monica Villamizar, Al Jazeera's correspondant in Bogota, said: "This boy has become the symbol of Colombia's tragedy and civil conflict for the past four decades.
"He was a victim of kidnapping the moment he was born, and he is a boy that was born of a politician and a guerilla fighter," she said.
The boy was taken out of his mother's care shortly after being born and after falling ill he was given to a family trusted by the group.
"This family took the boy to a state-run hospital when they realised he was too sick and his condition was worsening," she said.
"It was this hospital who decided to put the child in foster care, and gave the government custody over the child, because he obviously bore signs of abuse and torture."
But Venezuela has complained that its own team of specialists was not permitted to take blood samples from the boy to make its own confirmation of the DNA results.
The hostages were to be handed over to Chavez who had been trying to secure the release of a number of people held by Farc until his efforts were stopped by the Colombian government.
Emmanuel's name and other details of his life were revealed last year by a police officer who escaped from a Farc base in April 2006, after eight years in captivity.
He had sometimes been held in the same camps as Rojas and her son. Villamizar reported that the relatives of Clara Rojas, namely her mother and her brother, have expressed a wish to file for custody of the child.
Luis Carlos Restrepo, the Colombian peace commissioner, said: "We're enormously satisfied that this boy, who was held in terrible conditions, can today finally be reunited with his family."