The deal brokered by regime ally Russia would see fighters with the Jaish al-Islam rebel faction leave Ghouta's main town of Douma for opposition-held territory in northern Syria, the Syrian Observatory for Human Rights said.
There was no immediate confirmation from the rebels, but pro-regime newspaper Al-Watan quoted "diplomatic sources" as saying the agreement would see fighters give up heavy weapons and leave Douma for northern Syria.
The retaking of Eastern Ghouta would mark a major milestone in President Bashar al-Assad's efforts to regain control of territory seized by rebel factions during Syria's seven-year civil war.
Backed by Russia, Assad's forces have scored a series of victories over rebel forces in recent years, often through campaigns of siege, aerial bombardment and ground offensives that have drawn widespread international condemnation.
The Observatory, a Britain-based monitoring group, said Sunday's deal provides for Jaish al-Islam fighters and their families, as well as civilians who want, to be evacuated to rebel-held areas in the northern province of Aleppo.
It will also see Russian military police enter the town and government institutions return to the area, the monitor said.
Regime forces had already retaken more than 95 percent of Eastern Ghouta in a six-week air and ground blitz that forced tens of thousands from their homes.
Successive evacuation deals were reached with rebel forces in parts of the enclave, with more than 45,000 fighters and civilians bussed out in recent weeks. Tens of thousands of other civilians have fled to regime-held territory.
'Choice of dying or leaving'
More than 4,000 people left the devastated town of Harasta last week under a deal with the Ahrar al-Sham rebel group.
And more than 41,000 evacuated a southern pocket including the town of Arbin this week under another deal with the Faylaq al-Rahman opposition faction.
Earlier Sunday an agreement had been reached with civil authorities in Douma for hundreds of civilians to leave for Idlib, a northwestern province still largely outside regime control, the Observatory said.
A civilian committee taking part in the negotiations with Russia said a deal had been reached "to evacuate humanitarian cases to northern Syria". It gave no further details nor did it say when the planned evacuations would start.
The Observatory said evacuations were underway under that deal with civilians -- including of the sick or wounded, or family members of the Faylaq al-Rahman rebel group -- to head towards Idlib.
Talks with Jaish al-Islam for the evacuation of Douma had dragged on for several days, with residents growing nervous.
"Of course I would rather leave. There are no more homes here, not a single place to settle," said Abu Rateb, 30.
"But I won't go to regime-held areas to join ranks with the Syrian army," he said, adding he would prefer to go to Idlib.
Haitham, 38, a media activist who did not give his surname, said he would rather stay in his hometown.
"To abandon your home is to abandon your soul," he said. "But if they give us the choice of dying or leaving, it will be another matter."
Syria's army had on Saturday vowed to finish off rebels in Douma.
A statement said the military would press on with "fighting in the area of Douma to rid it of terrorism", in reference to the rebels.
The regime assault since February 18 has killed more than 1,600 civilians, the Observatory says, and devastated entire neighbourhoods.
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