Regime news agency SANA said: "Twelve buses carrying 629 Jaish al-Islam terrorists and their families exited Douma.in preparation of them being transported to Jarabulus", using the government's term for all rebel fighters.
The sources confirmed that the deal was instead similar to the one reached in Qaboun and Barza, which stipulated the evacuation of fighters opposed to a deal reached with the Syrian regime, and their families to the north of Syria.
The deal will see Russian military police enter Douma and government institutions return to the town, the monitor said.
There was no immediate comment from Jaysh al-Islam.
The BBC's Martin Patience in Beirut says it is not clear whether Jaysh al-Islam's fighters want to give up their weapons, and possibly become a security force under government control, or be bussed to a rebel stronghold in northern Syria.
Last week, two rebel groups reached an evacuation deal with the Russian army, which resulted in about 19,000 people leaving for the northern province of Idlib. On Sunday, 112 militants and 1,034 family members left Douma for the rebel-controlled Idlib province, the Reconciliation Center reports.
It gave no further details nor did it say when the planned evacuations would start.
The army said hundreds of rebels had been killed in the ferocious offensive.
The Syrian army has repeatedly said regaining control over rebel-held suburbs would stop rocket attacks on the capital.
La estación espacial china se precipita sobre la Tierra
Sin embargo , la estación también podría caer en cualquier punto de África, el sur de Asia y gran parte de Oceanía . Su ingreso a la atmósfera además ocasionaría que el objeto se disperse sobre miles de kilómetros.
Syria's war has killed more than 350,000 people and displaced millions since starting in 2011 with a brutal repression of anti-regime protests.
State media say 41,000 people have also been evacuated to Idlib under deals between Ahrar al-Sham and Faylaq al-Rahman.
The last rebels standing in the Damascus suburb of Ghouta were poised to leave on Sunday, Syrian state-affiliated media reported, cementing a significant victory for the government of President Bashar Assad.
Tens of thousands of other civilians have fled to regime-held territory.
Mr Trump has told advisers he wants an early exit of USA troops from Syria, two senior administration officials said on Friday, a stance that may put him at odds with U.S. military officials who see the fight against Islamic State as nowhere near complete.
The Syrian army last week warned the insurgents to surrender or face a military assault to drive them out.
The military offensive by Syrian government forces and their allies, which involved weeks of intense bombardment, has left more than 1,600 civilians dead and thousands more wounded in eastern Ghouta since February 18, according to the observatory.
Numerous predominantly Sunni Muslim inhabitants of eastern Ghouta say they fear their displacement was part of a deliberate attempt to bring demographic changes in strategic areas that dilutes their presence in favor of Assad's Alawite sect and other minorities.