The Syrian Army has wrestled back complete control of Homs city in the previous months - with the exception of al-Waer - and a year ago announced plans for rebuilding projects in several districts of the city.
Buses have begun transporting people out of al-Wair district, under a Russian-backed evacuation deal.
More than 1,500 people are expected to be evacuated from the neighbourhood of al-Waer on Saturday, including around 500 rebels, according to the Syrian Observatory for Human Rights.
The Syrian government described such deals as a "workable model" that would bring the country closer to peace after six years of conflict.
The deal had been negotiated between a Russian team and rebels, stipulating that around 12,000 people will leave al-Waer area, among them 2,500 fighters.
Officials say the exodus will take several weeks.
"We are optimistic that the full exit of armed [fighters] from this district will pave the way for other reconciliations and settlements", he said.
And no aid has reached the area in at least four months, with a United Nations convoy that attempted to reach Waer in February seized by gunmen who diverted the assistance to a government-held area. He added that he had not expected anything from Geneva, where United Nations -led peace talks ended this month with no breakthrough.More news: QB Geno Smith leaves Jets for Giants
Mr Barazi said 1,479 people, including 423 rebels, left Waer on Saturday.
"This agreement was reached only under the patronage of the Russian side. and it will be implemented with Russian guarantees", he said.
The men, women and children, majority carrying their belongings in suitcases and plastic bags, then boarded white busses that were to take them to the northern rebel-held town of Jarablous on the border with Turkey.
"Not a single weapon or fighter will be left in Waer", he said, adding that about 40,000 residents were expected to stay.
Dozens of buses stood at a crossing waiting to leave al-Waer, accompanied by SARC ambulances, a Reuters witness said.
Mr Barazi said there was communication with other rebel-held areas north of Homs city to reach similar deals.
The rebel fighters head to an area targeted in recent days by United States airstrikes.
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.