The footage shows the captives, who were captured between August 1998 and July 1999, greeting relatives and thanking those who are trying to negotiate their release.
"I miss you so very much and I keep you in my heart," Luis Arturo Arcia, one of the soldiers held captive, says in one video.
Some of the other captives made political comments, while some gave practical instructions to family members on how their salaries should be used.
General Oscar Gomez, chief of staff of the Colombian army, said the videos showed the "inhumane conditions" in which the hostages were being kept.
Prisoner swap refused
The Farc is Colombia's biggest armed group and is holding at least 24 soldiers and police officers.
The group has said that it will only release its captives in exchange for Farc members being freed from Colombian jails.
The government of President Alvaro Uribe has refused to consider prisoner swaps and called on the Farc to release its captives.
The Farc has been fighting against the Colombian authorities for 45 years, in Latin America’s oldest insurgency.