The Syrian government and other parties on the ground have agreed to allow 20 observers to be sent to east Aleppo to monitor evacuations, the UN spokesman said Tuesday.
The United Nations is however waiting for all sides to grant access for deliveries of humanitarian aid to Aleppo, where civilians have been living under siege since July.
The green light came a day after the UN Security Council adopted a resolution on deploying the monitors to oversee the evacuation and report on the protection of civilians who remain in the besieged city.
"We have received authorization to send 20 international and national staff to Aleppo to play a critical role in the monitoring and response in Aleppo city," said UN spokesman Stephane Dujarric.
"Access to people in need to provide them with life-saving humanitarian assistance is also urgently needed," he added.
At least 25,000 people have left rebel districts of Aleppo since the operation began last week, according to the International Committee of the Red Cross.
Syrian forces last week moved to assert full control over the east of the city, which had been held by opposition fighters since 2012.
The fall of Aleppo will hand President Bashar al-Assad his biggest victory in the nearly six-year war that has killed more than 310,000 and displaced half of the country's population.
A UN team is present at a Syrian government checkpoint in Aleppo to monitor the convoy of buses carrying evacuees en route to rebel-held territory, Dujarric said.
"Protection of civilians leaving these areas remains the biggest concern," said Dujarric.
"All remaining civilians must be allowed to safely leave should they choose to do so."
France, which drafted the resolution on the dispatch of observers, has said that the international presence could prevent another Srebrenica, the 1995 massacre of thousands of Bosnian men and boys when the town fell to Serb forces.