An AFP correspondent inside Qabun saw around 10 buses carrying out residents and fighters in the morning, after a deal for the neighbourhood was announced late Saturday following heavy fighting.
The agreement mirrors those implemented earlier this week in the nearby rebel-held districts of Barzeh and Tishrin.
State media announced the evacuation had started, and an activist inside the remaining opposition-held part of the district earlier confirmed preparations for the operation were underway.
"The buses are being prepared, they are waiting in the areas controlled by the regime," Odai Awdeh told AFP.
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The evacuation deal came on Saturday night after government forces advanced inside the neighbourhood.
"The Syrian army yesterday managed to encircle dozens of armed elements inside Qabun neighbourhood, forcing them to surrender and hand over their weapons," a source from the pro-regime National Defence Forces militia told AFP.
The deals for Qabun, Barzeh and Tishrin neighbourhoods follow a pattern of agreements under which the rebels agree to surrender in exchange for safe passage to opposition-held territory elsewhere.
The government says the deals are the best way to end the six-year war, but the opposition says it is forced into the agreements by regime bombardment and siege.
All three headed to Idlib province, in northwest Syria.
The negotiations on evacuating Qabun had stalled earlier this week over demands that some rebels be allowed to head to Eastern Ghouta, rebel-held territory outside Damascus.
But the National Defence Forces source and the Syrian Observatory for Human Rights monitor said the final agreement only allowed evacuees passage to Idlib.
Damascus has been insulated from some of the worst violence of Syria's war, which has killed over 320,000 people since it began with anti-government protests in March 2011.