Josue Daniel Calvo walked unaided from the helicopter
Colombian President Alvaro Uribe says he is not opposed to an exchange of jailed Farc rebels for hostages.
But he said any swap was conditional on freed rebels not returning to Farc ranks and their "criminal activities".
Mr Uribe was speaking after rebels freed Private Josue Daniel Calvo, who was kidnapped nearly a year ago.
Negotiators hope another soldier, Sergeant Pablo Emilio Moncayo, will be freed on Tuesday, after more than 12 years in captivity.
Pte Calvo, 22 was handed over by Farc guerrillas to a team of delegates from the International Committee of the Red Cross (ICRC) and mediator Senator Piedad Cordoba at a secret jungle location.
He was then flown to Villavicencio where he was reunited with his family.
"Happiness has returned to our home again," his father, Luis Alberto Calvo, said.
Speaking after a meeting of his security council, President Alvaro Uribe thanked all those involved in securing Pte Calvo's release.
Mr Uribe said that he did not oppose an accord allowing prisoner exchanges as long as it did not result in rebels leaving prison to reoffend.
Mr Uribe enjoys high approval ratings
"The government has facilitated releases, has carried out rescues and is not opposed to a humanitarian accord, as long as such an accord does not mean returning criminals to the Farc," he said.
And in a reference to a recent bombing blamed on the Farc, Mr Uribe said no peace deal was possible "while there is no end to criminal activities".
What was needed for an accord, he said, was "good faith".
Farc rebels are still holding some 20 police officers and soldiers as bargaining chips for the release of hundreds of jailed rebels.
There is unlikely to be any development on exchanging prisoners until the new president takes office in August.
Mr Uribe, who enjoys high approval ratings for his tough stance against the Farc, cannot stand again in May's presidential election.
After more than four decades of fighting, the Farc has been weakened but is still capable of carrying out ambushes and bombings, and remains a force in some rural areas.