Militants from the Islamic State jihadist group and its rival, Al-Qaeda's Syrian affiliate Al-Nusra Front, will reportedly quit the districts of Qadam, Hajar al-Aswad and the besieged Palestinian camp of Yarmuk.
"An agreement was reached whereby 4,000 fighters and civilians, including members of Al-Nusra and IS, would leave" the neighbourhoods on Saturday, one government official close to the negotiations said.
They would then be transported to the northern cities of Raqa, held by IS, and Marea which is controlled by Islamists and Al-Nusra, the official said.
The second phase of the deal would see government institutions reopen in the neighbourhoods and "the necessities of daily life would be secured", the official said.
It will be the first time in more than two years that market goods have been able to be sent in to the three southern districts, which have been under a crippling government siege.
IS militants attacked the Yarmuk Palestinian camp in April, fighting Al-Nusra units there for control.
The jihadists then overran parts of Qadam in August after launching an attack from their base in nearby Hajar al-Aswad.
Their advance into Qadam had brought them closer than ever to central Damascus.
The ceasefire deal comes after two months of intense negotiations between Syria's government and district leaders, the Syrian Observatory for Human Rights monitoring group said.
Speaking on condition of anonymity, one local leader in Qadam said that "every fighter will be allowed to leave with his family and one suitcase and his personal weapon".
- 'Larger reconciliation process' -
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The areas are already in the process of being demilitarised.
A Syrian army unit entered Qadam on Thursday to confiscate heavy weapons and military equipment used by the jihadists, a security source on the ground said.
Eighteen buses had also crossed into the neighbourhood in preparation for Saturday's evacuation, which would include "2,000 combattants, mostly jihadists", he added.
Local ceasefires have been implemented in other parts of Syria with varying degrees of success.
Typically, towns or villages under siege agree to a truce in exchange for humanitarian aid and the evacuation of wounded civilians and fighters.
A similar deal earlier this month in the central city of Homs saw 2,000 rebels and civilians leave the last opposition-held neighbourhood.
Mohammad al-Omari, a representative of Syria's reconciliation ministry, told AFP that the "first phase of the deal will have a positive effect on Yarmuk and all of the southern areas".
He said he hoped a "larger reconciliation process" would allow some 1.8 million people to return to the southern suburbs of Damascus.
More than 250,000 people have been killed since Syria's conflict erupted in 2011, and millions have fled their homes.
A United Nations representative in Damascus told AFP that the world body had no role in the negotiations or developments in the southern areas of the capital.
And Chris Gunness, spokesman for the UN's Palestinian refugee agency, said it was seeking "further details" about the deal.
"As UNRWA is deeply concerned about their well-being, the agency is seeking from the Syrian government further details of any negotiated arrangements that will affect the humanitarian situation of civilians in Yarmuk," he said in an email.