The bodies of Cpl. Salatiel Alvarez and an unnamed civilian were found abandoned along a road in the Palmira municipality in southwest Colombia, Colombia Reports said Monday.
Police said the victims appeared to have been killed about five days ago.
The Gabriel Galvis and Garipiari unit of FARC are alleged to have carried out the kidnappings.
FARC has not confirmed or denied the group's involvement.
The rebel group agreed last year to stop its kidnappings as a pre-condition for ongoing peace talks.
FARC is the Spanish acronym for the Revolutionary Armed Forces of Colombia.