The deal also provides for the evacuation to northern Syria of any rebels and jihadist fighters who refuse to live under government control.
Today afternoon, buses began taking civilians and armed fighters out of opposition-held territory through the town of Jaba, state television said. It said they would be taken north to Idlib which is under jihadist and rebel control.
The channel earlier reported more than 50 buses were prepared to ferry people north. Vehicles had been arriving in Syria's south since yesterday, said the Syrian Observatory for Human Rights.
"As the convoy of buses was gathering, one of the drivers lost control and four people, including two women, were run over and killed," said the Britain-based monitor.
Fighters then fired their weapons, wounding a bus driver. Observatory head Rami Abdel Rahman said it was still unclear exactly how many people would ultimately be evacuated.
Among them were members of Hayat Tahrir al-Sham (HTS), an alliance led by Al-Qaeda's onetime Syria affiliate which refused to sign up to the deal. Quneitra is a thin, crescent-shaped province wedged between the buffer to the west and Daraa province to its east.
One month ago, Syria's regime launched an operation to retake rebel areas in Daraa and Quneitra, using military force and surrender deals brokered by its Russian ally.
Fighting forced several hundred thousand people to flee, and as many as 140,000 remain displaced in Quneitra, according to the United Nations. The UN's humanitarian coordination office (OCHA) warned they are inaccessible to aid organisations based around an hour away in Damascus because of a lack of approvals.
Both Israel and Jordan, which shares a border with Syria, have kept their borders closed to the displaced. Israel seized 1,200 square kilometres (460 square miles) of the Golan during the Six-Day War of 1967, then annexed it in 1981 in a move never recognised internationally.
Some 510 square kilometres of the Golan remain on Syria's side of the ceasefire line, with a UN peacekeeping force overseeing a buffer zone stretching some 70 kilometres from Lebanon in the north to Jordan in the south.
Under the terms of the deal, a rebel source told AFP, Syrian and Russian forces are to enter the buffer zone.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)