The evacuation of Waer, a northwestern district of the city that has been under siege by the army for years, is the latest in a series of "reconciliation" deals struck by the government that the rebels say amount to starving them out.
It comes ahead of a new round of UN-brokered talks that open in Geneva on Thursday in an attempt to end the conflict that has killed more than 320,000 people and driven millions from their homes.
An AFP correspondent saw a first wave of three green buses carrying civilians including children as well as dozens of fighters, their rifles slung over their shoulders.
Throughout the day, women and children munching on pieces of bread lined up to load their luggage onto the buses, while men appeared to go through extra screening in separate lines.
Stern-looking Russian forces looked on, wearing green fatigues with black bulletproof vests emblazoned with the word "Police" on the front.
Barazi said evacuations were over for today and that a total of 1,479 people -- including 423 rebels -- had left.
"Not a single weapon or fighter will be left in Waer," he said, adding that about 40,000 residents were expected to stay in the district.
Three waves of rebels and their families had already left Waer under an agreement first reached in December 2015, but subsequent evacuations stalled.
In a new deal reached last week, government and rebel representatives agreed that up to 100 Russian troops would deploy inside Waer to oversee the final phase of evacuations.
"Russian forces came to Syria for this -- to help their friends and allow people to live safely in this country again."
Moscow is a decades-old ally of the Damascus regime, and in September 2015 launched an air campaign in support of President Bashar al-Assad's forces.
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