"An agreement has been reached for the evacuation of the residents of Aleppo, civilians and fighters with their light weapons, from the besieged districts of east Aleppo," said Yasser al-Youssef from the political office of the key Nurredin al-Zinki group.
He said the deal was "sponsored by Russia and Turkey" and would be implemented "within hours".
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The deal comes one month into a Syrian army operation to recapture all of east Aleppo, which rebels had held since 2012.
The rebels are now confined to just a small pocket of territory in the south of their former bastion, and tens of thousands of civilians have already fled former opposition territory during the army offensive.
"The first stage will be the evacuation of civilians and wounded, within hours, and afterwards fighters will leave with their light weapons," Youssef added.
The deal stipulates those leaving will be allowed to choose whether to go to rebel-held territory in west Aleppo province or to neighbouring Idlib province.
A source in the powerful Ahrar al-Sham rebel group also confirmed the deal, saying civilians and then fighters would be evacuated on buses to either western Aleppo province or Idlib.
Idlib province, in northwest Syria, is almost completely controlled by a powerful rebel alliance known as the Army of Conquest.
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