The Syrian regime has struck a number of deals with local rebels in the past, under which they evacuate for rebel-held parts of northern Syria, bordering Turkey.
The rebels in Idlib released four children and eight women they kidnapped from Kafraya and Foa, and returned the bodies of eight government forces men in exchange of the release of 19 rebels detained by the pro-government fighters in Kafraya and Foa.
The evacuation of Zabadani, also a part of the deal, was apparently delayed.
People from Foah and Kefraya, two government-held towns in the north-west, have arrived in Rashideen, west of Aleppo, AFP news agency reports.
The Syrian government and the opposition have begun a co-ordinated population swap of tens of thousands of people from four besieged towns. Another 3,000 people are expected to be bused out of Foua and Kfraya on Friday evening, according to Baghdadi.
The convoys from Madaya and Zabadani are to head for Idlib.
A member of one of the Shi'ite parties earlier said 60 buses were moving through the town of al-Foua.
"We just left now - around 2,200 people in around 65 buses", Madaya resident Amjad al-Maleh told AFP by telephone. State television reported that engineering teams and Syrian forces would soon enter the town. The convoys include hundreds of fighters from each side, the Observatory said.
The armed opposition fighting for six years to unseat Assad is mostly Sunni Muslim, like most of Syria's population.
Madaya and Zabadani, which are predominantly Sunni, have meanwhile been besieged since June 2015 by the Syrian army and fighters from Lebanon's Shia Islamist Hezbollah movement.
Assad achieved his most significant victory to date in December, driving rebels out of long-divided Aleppo.
The deal, which began on Wednesday following a delay, is an an exchange of prisoners between rebels and government forces.