Georgia says Russian troops have left "buffer zones" inside its territory adjacent to its breakaway regions of Abkhazia and South Ossetia.
Moscow has not confirmed the move, but President Dmitry Medvedev said the pullback would be complete by midnight, well ahead of a Friday deadline.
Russia's foreign minister said an EU mission monitoring the pullout would be excluded from the disputed regions.
Russia plans to keep nearly 8,000 troops in South Ossetia and Abkhazia.
Moscow has maintained a military presence in the region since ousting Georgia's army in August.
Russia has recognised Georgia's two breakaway regions as independent states - a move which has drawn strong condemnation from Georgia and Western leaders.
Fighting in the region began on 7 August when Georgia tried to retake South Ossetia by force after a series of lower-level clashes with Russian-backed rebels.
Russia launched a counter-attack and the Georgian troops were ejected from both South Ossetia and Abkhazia days later.
