State television said militants and their relatives had started departing Barzeh for Idlib province in northwest Syria.
The so-called Syrian Observatory for Human Rights, a British-based war monitoring group, said buses had arrived in Barzeh at dawn and hundreds of militants and family members had started to board them. More people would leave over the next five days, state TV and the Observatory said.
A military spokesman from the Jaish al-Islam group confirmed the evacuation had begun, but said his faction had not taken part in any negotiations about it. The spokesman, Hamza Birqdar, said the government had concluded the deal with a civilian committee in Barzeh.
Syrian President Bashar al-Assad has promoted the use of such evacuations, along with what his government calls "reconciliation" deals for rebel-held areas that surrender to the government, as a way of reducing bloodshed.
Barzeh, at the northeast edge of Damascus and near the rebel-held Eastern Ghouta pocket of towns and farms, has been the site of intense fighting in recent months.
On Sunday, the Syrian army advanced under intense bombardment in the Qaboun district, which adjoins Barzeh in the same besieged enclave, the Observatory said.
In recent months, hundreds of militants have laid down weapons and surrendered to the Syrian army under such agreements.
Syria has been grappling with militancy since March 2011. UN Special Envoy for Syria Staffan de Mistura estimated last August that more than 400,000 people had been killed in the conflict until then.
