Gamsakhurdia, Georgia's first post-Soviet president, was overthrown in a popular uprising in January 1992.
Gamsakhurdia fled to Chechnya and later returned to Georgia to lead an unsuccessful rebellion.
He died in western Georgia under mysterious circumstances in 1993.
Gamsakhurdia's widow, Manana Archvadze-Gamsakhurdia, has in the past said he committed suicide after being surrounded by troops loyal to his rival -- former Georgian President Eduard Shevardnadze. More recently she and some of Gamsakhurdia's relatives have said he was assassinated.
Georgian officials say Gamsakhurdia's own supporters shot him after an argument.
Archvadze-Gamsakhurdia had complained in late last November that the former leaders grave in the courtyard of a home he occupied while living in exile in Grozny had been destroyed and that the whereabouts of his remains were unknown.
Russian officials tracked down Gamsakhurdia's remains at the request of his son, Tsotne.
The discovery of Gamsakhurdia's apparent remains could help solve the mystery surrounding his death.