This development came as the Syrian army has so far captured over 90 percent of Eastern Ghouta in an offensive that has been dragging on since late last month.
The agreement will also see the release of kidnapped people by the rebels and lists of names were handed over to the Russian side, the report said.
The rebels and members of their families were transported by 52 buses from the outskirts of the town of Arbeen in Eastern Ghouta toward rebel-held areas in northwestern Syria.
According to the deal, some 7,000 rebels and their family members will leave areas of Jobar, Zamalka, Arbeen, and Ayn Tarma in the central part of Eastern Ghouta, and the deal covers the main rebel groups in control of those areas, namely the Failaq al-Rahman, and the al-Qaida-linked Nusra Front.
Eastern Ghouta, a 105-square-km agricultural region consisting of several towns and farmlands, poses the last threat to the capital due to its proximity to government-controlled neighborhoods east of Damascus and ongoing mortar attacks that target residential areas in the capital, pushing people over the edge.
The UN humanitarian agencies have sounded the alarm about the worsening humanitarian situation for 400,000 people in that region, where activists said around 1,000 people have been killed since late last month by the heavy bombardment and military showdown in areas of Eastern Ghouta.
As the Syrian army advanced in Eastern Ghouta, tens of thousands of civilians have fled toward government-controlled areas for the first time in six years, with activists placing the number of the civilians that have so far left at 140,000, according to the Syrian Observatory for Human Rights.
The fresh deal comes a day after the Failaq al-Rahman group declared a unilateral cease-fire to negotiate its withdrawal from the region.
The evacuation is part of a recently-reached deal between the rebels and the Syrian army under the Russian mediation.
DAMASCUS, March 25 (Xinhua) -- A total of 3,708 rebels and their family members evacuated Syria's Eastern Ghouta area on Sunday, as the second batch to leave areas under the control of Failaq al-Rahman militia, state TV reported.
Four major rebel groups are currently positioned inside Eastern Ghouta, namely the Islam Army, Failaq al-Rahman, Ahrar al-Sham, and the Nusra Front.
These areas have been the launching pad for firing mortar and rocket shells on the Syria capital of Damascus throughout the last seven years of crisis.
This is the second batch to leave areas under the control of Failaq al-Rahman, a day after 981 rebels and their families evacuated toward rebel-held areas in Idlib province in northwestern Syria.