Earlier this year conditions there were so bad that, amid reports of the army burning local wheat fields, some people were reduced to eating grass and sending their children out to beg, the UN’s World Food Programme said.
Insurgents and government forces agreed a deal on Thursday to evacuate the town, which the Syrian army has surrounded since 2012. The UN said only one shipment of aid has reached the area since then.
A Reuters witness saw six buses leaving the town. Footage on state television showed buses carefully driving past a large group of soldiers through streets lined with rubble.
Peeping from the window of one of the vehicles was a small child no older than four or five, too young to remember life before the siege.
A first group was later reported to have arrived at a housing centre in Herjalleh, another suburb west of Damascus, by Syrian state television.
A Syrian Army general told reporters in Daraya that around 300 families of fighters would leave the town by last night, and in total around 700 fighters and 4,000 civilians would be evacuated today.
Two Free Syria Army rebel groups, the Shuhada al-Islam and Ajnad al-Sham, will travel today to Idlib, a rebel stronghold in northwest Syria.
The plight of civilians in Daraya and other besieged areas has long been of concern to the United Nations, which has condemned the use of starvation as a weapon by both sides
However, the United Nations was not consulted on Daraya’s evacuation plan and UN Special Envoy Staffan de Mistura and UN humanitarian co-ordinator Stephen O’Brien voiced deep concern about it.
They said civilians should be evacuated only if their safety could be guaranteed and it was on a voluntary basis.
There have been previous deals to allow similar evacuations of besieged fighters and civilians, or to let people return to their homes after ceasefires were agreed.