Emmanuel was born in April 2004 and taken from her while she was held captive by Farc, or the Revolutionary Armed Forces of Colombia, in the country's jungles.
Emmanuel, whose father is a Farc fighter, was handed over to Rojas by the Colombian Family Welfare Institute, a local government organisation.
Elvira Forero, the institute's director, said Emmanuel had undergone psychological counselling for the meeting and would not go home with his mother right away.
Rojas, 44, only found out her son was alive in a New Year's Eve radio broadcast
Rojas, an aide to Ingrid Betancourt, the French-Colombian politician still being held by Farc, was greeted by Colombia's defence minister and chief peace negotiator.
"I am extremely moved to be back in my land ... I feel like I've been reborn, I am living again," she said.
Rojas said "this is not a total happiness because many [hostages] remain and we are waiting for them".
Reporting from Bogota, Al Jazeera's Monica Villamizar said Rojas revealed that she and Betancourt escaped their captors and were in the Colombian jungles for three days before being recaptured.
|Gonzalez was also released on Thursday [EPA]|
The failed escape affected their friendship as the two blamed each other, she said.
Villamizar said Emmanuel was removed from her care at eight months because he had contracted a tropical illness and needed medical attention.
But the promised 15-day separation turned out to be three years.
A peasant delivered him to Colombian social services, which - unaware of his identity - placed him in a foster home in Bogota
where he has been for the past two years.
Meanwhile, Chavez said on Sunday that he would try to persuade the Farc rebels to lay down their weapons if Colombia's US-backed government allows him to meet with the rebels' commander.
Chavez also accused Washington of fomenting Colombia's decades-old armed conflict, saying that unceasing warfare provides "the perfect excuse" to maintain a military presence in the Andean nation, which has received billions of dollars in military aid from the US.
"I don't agree with the armed struggle, and that's one of the things I want to discuss with [rebel leader Manuel] Marulanda," he said on his weekly TV programme.
Chavez also urged Alvaro Uribe, his Colombian counterpart, to recognise Farc and the National Liberation Army as legitimate groups - rather than terrorists - as a first step towards possible peace talks.
Source: Al Jazeera and agencies