Rebels announced earlier they had gained full control of the key city of Homs after only a day of fighting
Syrian President Bashar Al Assad boarded a plane and left Damascus for an unknown destination on Sunday, two senior army officers told Reuters, as rebels said they had entered the capital with no sign of army deployments.
Thousands in cars and on foot congregated at a main square in Damascus waving and chanting "Freedom", witnesses said.
"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.
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Sednaya is a large military prison on the outskirts Damascus where the Syrian government detained thousands.
Just hours earlier, rebels announced they had gained full control of the key city of Homs after only a day of fighting, leaving Assad's 24-year rule dangling by a thread.
Intense sounds of shooting were heard in the centre of the Damascus, two residents said on Sunday, although it was not immediately clear what the source of the shooting was.
The fall of Homs gives the insurgents control over Syria's strategic heartland and a key highway crossroads, severing Damascus from the coastal region that is the stronghold of Assad's Alawite sect and where his Russian allies have a naval base and air base.
Homs' capture is also a powerful symbol of the rebel movement's dramatic comeback in the 13-year-old conflict. Swathes of Homs were destroyed by gruelling siege warfare between the rebels and the army years ago. The fighting ground down the insurgents, who were forced out.
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".
Rebels freed thousands of detainees from the city prison. Security forces left in haste after burning their documents.
Residents of numerous Damascus districts turned out to protest Assad on Saturday evening, and security forces were either unwilling or unable to clamp down.
Syrian rebel commander Hassan Abdul Ghani said in a statement early Sunday that operations were ongoing to "completely liberate" the countryside around Damascus and rebel forces were looking toward the capital.
In one suburb, a statue of Assad's father, the late President Hafez Al Assad, was toppled and torn apart.
The Syrian army said it was reinforcing around Damascus, and state television reported on Saturday that Assad remained in the city.
Outside the city, rebels swept across the entire southwest over 24 hours and established control.
Qatar, Saudi Arabia, Jordan, Egypt, Iraq, Iran, Turkey and Russia issued a joint statement saying the crisis was a dangerous development and calling for a political solution.
But there was no indication they agreed on any concrete steps, with the situation inside Syria changing by the hour.
Syria's civil war, which erupted in 2011 as an uprising against Assad's rule, dragged in big outside powers, created space for jihadist militants to plot attacks around the world and sent millions of refugees into neighbouring states.
Hayat Tahrir al-Sham, the strongest rebel group, is the former al Qaeda affiliate in Syria regarded by the U.S. and others as a terrorist organisation, and many Syrians remain fearful it will impose draconian Islamist rule.
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