The advance, after heavy bombing from the air, is a major blow for the armed opponents of President Bashar al-Assad.
State TV said government troops were dismantling mines and explosives and continuing their advance.
Thousands of civilians have fled the besieged districts after a weekend of heavy fighting. Hundreds of families have been displaced.
Rebel fighters have been driven out of more neighbourhoods of their long-held enclave in eastern Aleppo, as Syrian government forces continue to advance.