He added that he had not expected anything from Geneva, where United Nations -led peace talks ended this month with no breakthrough.
Between 10,000 and 15,000 rebels and civilians would evacuate in batches over the coming weeks under the deal, according to opposition activists in al-Waer and a war monitor.
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.
The Governor added that the first group includes the evacuation of more than 1500 gunmen and members of their families towards the northeastern countryside of Aleppo province, pointing out that the Syrian Arab Red Crescent (SARC) and the Syrian and Russian military police supervise the process.
Barazi said evacuations were over for Saturday and that a total of 1,479 people - including 423 rebels - had left.
"We are optimistic that the full exit of armed (fighters) from this district will pave the way for other reconciliations and settlements", he said. Hundreds of rebels have previously left al-Wair under its terms, but implementation of the agreement had stalled in recent months.
It followed earlier evacuation deals between rebels and government forces that were not fully implemented.
As the Syrian military continues their offensive against Islamic State (IS, formerly ISIS/ISIL), Damascus has intensified its efforts to persuade some of the rebel groups to surrender and sign reconciliation agreements.
"Russian forces came to Syria for this - to help their friends and allow people to live safely in this country again".
Homs became a key battleground of the Syrian uprising after residents embraced the call to overthrow President Bashar al-Assad in 2011 and drove security forces out of much of the city the following year.
Rebels and civilians have poured into Idlib at an accelerating rate over the past year, bussed out of other parts of western Syria that the government and allied forces recaptured from rebels.
The Syrian Observatory for Human Rights estimated that about 12,000 people, 2,500 of them rebels, will leave under the deal.
Waer district has been under a siege by regime forces for four years.