Defence ministry sources told media that Alfonso Cano had been killed in an army operation in the mountains in the south-west of the country. Details of the military operation in Cauca state are still sketchy, with some reports suggesting that Mr Cano was killed in a bombing raid.
State Governor Gonzalez Mosquera later told local radio that the military had "achieved one of its most important goals".
"The fingerprints matched," one senior security official was later quoted as saying by the Associated Press news agency.
Mr Cano, a 62-year-old academic from Bogota, became the Farc's leader in 2008 after his predecessor, Manuel Marulanda died of a heart attack.
Mr Cano's real name is Guillermo Leon Saenz.