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.
Foreign Minister Sergey Lavrov said European Union observers would be excluded from the disputed regions.
Russia will post nearly 8,000 troops in South Ossetia and Abkhazia.
Moscow has kept troops 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.
Georgia's interior ministry spokesman Shota Utiashvili said: "We can confirm that from the so-called buffer zones the withdrawal is complete."
Speaking earlier at an international security conference in France, Mr Medvedev said Russia wanted some 200 EU observers in the area to "act as guarantors" to prevent any further hostilities.
Mr Lavrov told the BBC that Russia believes the EU monitors would ensure security in the buffer zones.
"This is a European Union matter. We trust them," he said.
However, Mr Lavrov said that EU monitors would not be allowed to deploy in the two breakaway regions where Russia plans to maintain an 8,000-strong force.
Pullout 'on track'
A number of Russian armoured personnel carriers were seen heading towards South Ossetia earlier on Wednesday.
Russia's foreign minister on the withdrawal
The commander of Russian troops on the ground said military personnel had already withdrawn from five out of the six checkpoints in the area, and that the process would be completed by the end of the day.
"Everything is completely on track. Everything will be noted and registered in documents," Maj Gen Marat Kulakhmetov said.
The BBC's Mark Mardell, who is in Giro in Georgia, said he saw a convoy of three lorries, three tanks and an armoured vehicle roll out of one checkpoint.
As soon as they were gone the Georgians came in - one man and his small boy put a Georgian flag up on the post where they had been, our correspondent said.
The pull-back was agreed in a ceasefire deal brokered by French President Nicolas Sarkozy in early August.
The EU wants its observers to have access to the breakaway regions, but Russia has repeatedly refused to guarantee that.
The fighting in the region began on 7 August when Georgia tried to retake South Ossetia by force after a series of lower-level clashes. Russia launched a counter-attack and the Georgian troops were ejected from both South Ossetia and Abkhazia days later.