The armed opposition fighting for six years to unseat Assad is mostly Sunni Muslim, like most of Syria's population.
More than 30,000 people are expected to be evacuated under the deal, which began on Wednesday with an exchange of prisoners between rebels and government forces. They include former fighters, activists and medical workers who say they can not redeploy with the military that once shelled their homes, and who are wary of the treatment they will receive at the hands of the government's notorious security services.
Buses carrying mostly Sunni opposition fighters and their families simultaneously left the town of Madaya near Damascus, encircled by regime forces and their allies, but were still passing through regime-held areas, the Observatory said.
The Syrian Observatory for Human Rights confirmed the beginning of the evacuation.
Madaya and Zabadani are the latest in a constellation of towns once held by the opposition around Damascus to submit to government rule.
Civilian residents of Madaya and Zabadani will reportedly be allowed to remain if they choose.
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Mr Capriles said that he would appeal against the decision and stay in his job as governor, which he has held since 2008. CGTN's Juan Carlos Lamas reports from Caracas. "Plus the economic situation is insufferable, no one can live here".
A member of one of the Shi'ite parties said 60 buses were moving through the town of al-Foua. State television reported that engineering teams and Syrian forces would soon enter the town. During the attack more than 80 people were killed. The convoys include hundreds of fighters from each side, the Observatory said.
Amer Burhan, the director for Zabadani's field hospital, said he expects the young fighters in Zabadani to join the fronts in northern Syria to fight the government some more.
Critics say the population movements are permanently changing the ethnic and religious map, but in an exclusive interview with AFP on Wednesday President Bashar al-Assad insisted they were only temporary and people would return to their homes once the "terrorists" had been defeated. Rebels and Islamist factions have fought back and achieved recent advances in some areas.
Syrian Red Crescent ambulances carry the sick and wounded from government-held towns to the rebel-held Rashideen, west of Aleppo.
Assad achieved his most significant victory to date in December, driving rebels out of long-divided Aleppo.
The exit of 45 more buses from Foua and Kefraya has been postponed until Friday night due to time limits.
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