The UN Security Council has voted unanimously to "carry out adequate, neutral monitoring and direct observation" of the evacuations in eastern Aleppo.
The 15-member council demanded all parties in the conflict to provide UN officials and others with a "safe, immediate and unimpeded access" to those who remain in the Syrian city.
Since midnight, some 4,500 people have left the besieged rebel-held enclave of the city to surrounding villages.
Tens of thousands of civilians desperate to leave Aleppo were left stranded for 48 hours over the weekend after a ceasefire deal broke down.
Dubbed the People's Convoy, aid workers intend to take medical supplies to a new children's hospital in Syria.
Watch all of ITV News correspondent Dan Rivers' reports on the end of the battle for Eastern Aleppo and the evacuation from the city.