The deal was struck with the Failaq Al-Rahman militant group following the Russian Reconciliation Center for Syria-sponsored negotiations, the Russian military said on Sunday.
Around 1,000 fighters and their relatives left on Saturday, Syrian state news agency SANA said.
Eastern Ghouta's largest city Douma remained the only part still under rebel control.
Before the recent offensive, the suburb had an estimated population of 400,000.
The Syrian Army, reportedly gained control of 90 per cent of the territory in Eastern Ghouta, considered the main opposition stronghold near Damascus, in a month-long government offensive to take the area.
OPT: Palestinian child activist Ahed Tamimi sentenced to 8 months in prison
Israel disputes that its settlements are illegal and says their future should be determined in peace talks with the Palestinians. Ahed was arrested in the middle of the night at her home in the occupied West Bank village of Nabi Saleh on December 19.
Magnitude 6.6 quake strikes Papua New Guinea
As per reports by Daily Mail, the natural disaster was recorded 150kms east of Kimbe, in the province of West New Britain. In PNG, the last major natural disaster was reported earlier in the month, which claimed lives of 55 individuals.
United States firm increases cash offer for GKN's automotive business
American manufacturer Dana has increased its offer to combine with Redditch-based GKN's driveline division by $140m (£100m). Analysts predict the deal will go down to the wire. "I welcome Dana's announcement today".
Over 113,000 people have left the besieged Syrian district of Eastern Ghouta in nearly a month since the start of a Russia-backed humanitarian operation, according to a monitoring center affiliated with Russia's Defence Ministry.
The truce was put in place in order to facilitate Russian-brokered negotiations between the Assad regime and Jaish al-Islam rebels over a purported peace deal.
Moscow and Damascus say the Ghouta campaign is necessary to halt deadly rebel shelling of the capital.
Thousands of rebel fighters and their families have left three eastern Ghouta pockets in the past few weeks, after years of siege and weeks of heavy bombardment by the Syrian army and Russia's air force.
On Monday morning, the third round of evacuees from Arbin, Zamalka, Ain Terma and Hazza towns arrived in northern Syria after leaving the enclave overnight in a convoy of 94 buses, carrying some 6,000 civilians and Faylaq al-Rahman rebels according to al-Araby al-Jadeed.
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