The 15-member council unanimously adopted a French-drafted resolution that "demands all parties to provide these monitors with safe, immediate and unimpeded access."
With Russia's backing, the United Nations Security Council on Monday unanimously called for UN officials and others to be able to monitor evacuations from eastern Aleppo and the safety of civilians who remain in Syria's once largest city.
The 15-member council adopted a French-drafted resolution that "demands all parties to provide these monitors with safe, immediate and unimpeded access."
The step marks the first show of unity in months among world powers grappling with the crisis in Syria.
A rescue operation for thousands of civilians besieged by the Syrian regime and opposition forces continues, with convoys carrying those trapped in eastern Aleppo having reached relative safety.
Turkish Foreign Minister Mevlut Cavusoglu said some 20,000 people have been evacuated from Aleppo's east so far.
Buses that left from the Shia villages of Foua and Kefraya, north of Idlib, have also reached their designated stop in regime-held territory.
The exchange underscores the highly sectarian nature of the conflict, with Sunni-led rebels on one side and Shia Syrians loyal to the Iran-backed regime of Bashar al Assad on the other. The war, now entering its sixth year, has killed almost 500,000 people.
The evacuation of civilians, including wounded, from two predominantly Shia villages that have been besieged by rebels for years, was a condition for the Syrian army and its allies to allow thousands of fighters and civilians trapped in Aleppo to leave, under a deal brokered by Russia and Turkey.