This is the first stage of militants' leaving this area of the country.
"Before leaving, the militants blew up their headquarters and burned down everything that was inside them. They also destroyed the cemetery, damaging graves," the source said.
The source also noted that the buses that would take the militants to Idlib, as well as the vehicles of the Syrian Red Crescent, were waiting in the southwestern suburb of Damascus.
The militants' withdrawal was supposed to start on Thursday but was delayed.
Earlier this year, Syrian authorities and militant groups in various parts of the country reached agreements, where militants and their families would leave particular areas in stages with a guaranteed safe passage, courtesy of Syrian government troops.