The Syrian Observatory for Human Rights confirmed the news, saying that a deal brokered by regime ally Russian Federation would see fighters with the Jaish al-Islam faction leave Ghouta's main town of Douma for opposition-held territory in northern Syria.
The retaking of eastern Ghouta would mark a major milestone in President Assad's efforts to regain control of territory seized by rebel factions during Syria's seven-year civil war.
Syria's army had on Saturday vowed to finish off rebels in Douma.
The government's key ally Russian Federation announced on Sunday that Jaysh al-Islam had agreed to an evacuation.
A council member of Douma in Eastern Ghouta has said reports of a deal to surrender the opposition-controlled town to the Syrian government are not true.
Jaish al Islam, most of whose members are drawn from the area, has been defending the city of Douma against a months-long onslaught by government forces.
Jaish al Islam did not confirm the report; Saudi news broadcaster Al Arabiya said that a hard-line faction within the rebel group had rejected all negotiations and was insisting on fighting "to the end".
Douma is the last rebel-held area in Eastern Ghouta, after other towns in that sprawling countryside have seen the evacuation of all the rebels and their families toward Idlib province in northwestern Syria.
The Syrian army statement said the fall of Eastern Ghouta will restore security in Damascus and to roads connecting it to central, northern and eastern Syria.
In video footage published by Jaish Al Islam online on Sunday, the group's leader told a group of men in a mosque he would stay put.
Kevin Love (concussion) ruled out tonight vs. Hornets
But Cleveland's 79 points were a season-low and they endured their 14th straight defeat at Miami's AmericanAirlines Arena. They led by as many as 15 points in the first half, and were clinging to a two-point lead going into the fourth quarter.
The agreement, brokered under the stewardship of Russian Federation, a staunch Assad ally, called for the fighters to abandon their heavy weapons and depart to the city of Jarablus on Syria's northern border that is controlled by Turkish-backed rebels.
Since Feb. 19, more than 1,400 people have been killed in attacks by the regime and its allies in Eastern Ghouta, according to local civil-defense sources.
No date was given for the pullout and Moscow said rebels were expected to demine buildings and clear roadblocks before leaving.
Backed by Russia, Assad's forces have scored a series of victories over opposition forces in recent years, often through campaigns of siege, aerial bombardment and ground offensives that have drawn widespread global condemnation.
At least 46,000 people have been evacuated from Eastern Ghouta since the evacuation process began on March 22.
Since starting their assault mid-February, Assad's forces have retaken 95 percent of Eastern Ghouta, according to the Observatory.
More than 4,000 people also left the devastated town of Harasta last week under a deal with the Ahrar al-Sham rebel group.
An old woman dressed head-to-toe in black stood by a pile of suitcases, with a child wearing a winter coat and colorful backpack by her side.
Tens of thousands of rebels and civilians have been relocated to Idlib over the past years from different parts of Syria making it one of the most inhabited regions in the country.
- Orange County Joins Lawsuit Against California for Sanctuary Laws
- Declan Donnelly and Wife, Ali Astall, Are Expecting Their First Child
- President's attorney floated idea of Flynn, Manafort pardon
- Ball-tampering scandal: Key takeaways from Cricket Australia's sanctions
- Manchester United 2-0 Swansea City
- US To Probe Tesla Crash In California
- Best bets for Villanova-Michigan
- Chinese Space Station could Crash in Michigan This Weekend
- Kidd, Nash, Hill, Cheeks make Hall of Fame
- Briton charged over assault that left Australia rugby captain in hospital