The truces come more than a year into fierce daily battles in and around several areas of the city that have led to rebels and President Bashar al-Assad's forces deciding to compromise, with neither side able to claim victory.
In addition to Babbila, deals have been struck for local ceasefires in Qudsaya, Moadamiyet al-Sham, Barzeh, Beit Sahem, Yalda and Yarmuk Palestinian refugee camp.
The accords are negotiated by public personalities from disputed areas, including businessmen and former ministers.
A new agreement is reported to be in the offing for Harasta, a rebel bastion northeast of Damascus, and talks over Daraya southwest of the capital are also taking place.
An AFP journalist visiting Babbila accompanied by official regime escorts today saw dozens of cheering residents chant: "One, one, one! The Syrian people are one!"
Journalists saw streets completely destroyed by bombardment and fire. On Babbila's main street, every single building had been either destroyed or damaged.
Armed rebels were still present in the area, as the terms of the agreement also included an amnesty, a security source said.
According to the Syrian Observatory for Human Rights, rebels and regime loyalists have even set up joint checkpoints in some areas such as Qudsaya.
Syria's nearly three-year war is estimated to have killed more than 140,000 people and forced millions more to flee their homes.
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