The evacuation comes a week into a Lebanese army campaign against the group on the Lebanese side of the border, coinciding with a joint Syrian army and Hezbollah offensive in neighbouring Syrian territory.
Under the evacuation deal, several hundred jihadists and their families on both sides of the border are set to leave by bus for Deir Ezzor in eastern Syria, the country's only province still under IS control.
Todasy, Hezbollah and Syrian state television said that "buses transporting IS fighters have left the (Syrian) region of Qara, in western Qalamun, and are heading for the town of Albu Kamal in Deir Ezzor".
Earlier, a Lebanese army source told AFP that no convoys would leave the area until DNA tests had been carried out on bodies found in the region at the weekend, believed to be the remains of eight Lebanese soldiers IS kidnapped in 2014.
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It said today it had seized most of the territory formerly held by the jihadists. Six Lebanese soldiers have been killed in mine blasts since the campaign began.
The Lebanese army and Hezbollah announced a ceasefire on both sides of the border after reaching the evacuation deal over the weekend.
The war ravaging Syria has overflowed into Lebanon on several occasions.
IS has claimed several deadly bombings, clashed with the army and Hezbollah as well as winning a foothold in the mountainous east of the country.
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