Last Monday, a reconciliation agreement was reached in al-Waer neighborhood in Homs city providing for settling the situation of the gunmen in the neighborhood and the evacuation of those who reject the settlement with their families, paving the way for the return of the state institutions, in coordination between the security and military committee in Homs and the Russian reconciliation center in Hmeimim-base.
The Syrian Observatory for Human Rights estimated that about 12,000 people, 2,500 of them rebels, will leave under the deal.
It followed earlier evacuation deals between rebels and government forces that were not fully implemented.
The evacuation operation is being overseen by Syrian and Russian military police units, al-Barazi later told Reuters, adding that all rebels from al-Waer are due to depart within around six weeks.
Completion of the Waer agreement will bring Homs city -once known as the "capital of the revolution" - under the full control of Syrian President Bashar al-Assad.
"The preparations and the reality on the ground indicate that things will go well", the governor stressed.
Rebels will be bussed to opposition-held parts of Homs province, the town of Jarabulus on the Syrian-Turkish border or the northwest province of Idlib.
The government has agreed "reconciliation" deals for several rebel-held areas, and touts such agreements that grant safe passage to surrendering fighters as key to ending six years of war. But the opposition decries them as a tactic of forcibly displacing people who oppose Assad after years of bombardment and siege.
The Syrian Arab Red Crescent, along with Russian and Syrian officials are supervising the Al-Waer evacuation.
"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. Police officers searched people before the buses drove out, the Homs police chief told Syrian state television, which said 11 buses had left so far. "For years, it has besieged us.and bombed people's homes".
That backing has helped government forces recapture swathes of territory, including the whole of second city Aleppo as well as the famed desert city of Palmyra.