The Syrian president has left Damascus on a plane for an unknown destination, two senior Syrian army officers have told the Reuters news agency.
Hours earlier, rebels announced they had gained complete control of the key city of Homs after only a day of fighting.
Their lightning offensive threatens to end Bashar al Assad's 24-year rule.
Thousands of Syrians, in cars and on foot, have congregated at a main square in the city chanting for freedom, according to Reuters.
In Homs, thousands of residents poured onto the streets after the army withdrew from the city, dancing and chanting "Assad is gone, Homs is free" and "Long live Syria and down with Bashar al Assad".
The country's international airport in Damascus has been abandoned and rebels say they have entered the notorious Saydnaya military prison north of the capital and freed prisoners there.
"We celebrate with the Syrian people the news of freeing our prisoners and releasing their chains and announcing the end of the era of injustice in Sednaya prison," said the rebels.
Gunfire has been reported in the centre of Damascus, two residents said to Reuters on Sunday, although it was not immediately clear what the source of the shooting was.
Protesters on Saturday brought down a statue of the president's late father in a main square in a suburb a few miles from the centre of the capital.
This is the first time rebels have reached the city since 2018, and on Saturday, the UK-based Syrian Observatory for Human Rights, an opposition war monitor, said insurgents are now active in three Damascus suburbs, including Maadamiyah, Jaramana and Daraya.
The rebels were also reported to be marching from the east of the war-torn country towards Damascus's suburb of Harasta, in a shock offensive which began last week with the capture of Aleppo, in the north and the country's second biggest city, and Hama, in central Syria.
Hayat Tahrir al-Sham commander Abu Mohammed al-Golani, the main rebel leader, called the capture of Homs a historic moment and urged fighters not to harm "those who drop their arms".
They have also claimed Deir el Zor in the east, Suweida, Quneitra and Deraa in the south.