The Syrian Red Crescent posted a video on its Twitter page showing the convoys resuming work after receiving the necessary entry approvals.
It said "it will never stop trying to reach and alleviate the suffering of the vulnerable Syrians everywhere."
The convoy had been stalled at the Saraqib border crossing since Wednesday waiting for a green light from "all parties" to enter the rebel-held province of Idlib and neighbouring Aleppo.
The parts of Idlib and Aleppo where the aid is to be delivered are controlled by the Al-Qaeda splinter group Hayat Tahrir Al-Sham, or Turkish-backed rebels, while Saraqib is under the Syrian regime’s command.
The regions are the most badly affected by the devastating 7.8 earthquake which struck southeast Turkey and northwest Syria last month, which has so far killed over 52,000 people.
The disaster has left millions already reeling under years of conflict and an economic crisis in desperate need of aid.