The Russian military contingent will reportedly be withdrawn from all parts of Syria, except for the strategic Hmeimim air base and the Tartus naval base on the Mediterranean coast.
Russian soldiers will first be transported to areas controlled by the Turkish army and then flown back to Russia.
This follows an earlier report by the Russian propaganda agency TASS on the same day that Bashar al-Assad and his family had arrived in Moscow and been granted asylum "out of humanitarian considerations."
Clashes between forces loyal to Syrian dictator Bashar al-Assad and opposition armed groups began on Nov. 27 in the rural areas of Aleppo province in northern Syria. The offensive developed rapidly, with rebels capturing city after city.
On the morning of Dec. 8, opposition forces entered Damascus without a fight.
Bashar al-Assad has ruled the country for 24 years, succeeding his father Hafez al-Assad, who seized power in a military coup in 1970.
A revolution began in Syria in 2011, which escalated into a civil war involving the opposition, radical Islamists, and the Assad regime, which was supported by Russian troops.