The residential district became a symbol of resistance to Assad after government troops surrounded it with tanks and artillery and shelled it intensively for weeks, killing and wounding civilians cowering in its ruined buildings.
Rebels withdrew on Thursday in a key moment in the year-old uprising. An official at Syria's Ministry of Foreign Affairs and Expatriates said the army had "cleansed Baba Amro from the foreign-backed armed groups of terrorists."
Activists said Syria's army had begun hunting down and killing insurgents who had stayed to cover their comrades' retreat, although the reports could not be verified. They said 10 young men were shot dead on Friday.
In Geneva, the United Nations human rights body reminded Assad of his obligations under international law. "We are alarmed at reports starting to come out of the Baba Amro district of Homs after it was taken over by government forces yesterday," spokesman Rupert Colville said.
Rami Abdelrahman, from the Syrian Observatory for Human Rights, said Syrian troops had entered Ain al-Baida, near the Turkish border and 100-150 rebels had fled the area.
One pro-government figure said troops had "broken the back" of the uprising and the rebel withdrawal heralded impending victory over what he termed a Western-backed insurgency.
In Beirut, the International Committee of the Red Cross (ICRC) said Syrian authorities had agreed that the Syrian Arab Red Crescent and the ICRC could enter Baba Amro to evacuate casualties and to take food and medicine to civilians trapped by the fighting and siege.
"We have positive indications from the Syrian authorities to go in. We are ready to enter Baba Amro to evacuate first the sick and wounded and to take food and medical supplies," Samar al-Kadi, ICRC spokeswoman in Beirut, told Reuters.
The ICRC later said a convoy had reached Homs and was preparing to enter Baba Amro. The rebel Free Syrian Army (FSA) said on Thursday it was leaving the district -- normally home to 100,000 residents. Only a few thousand people remain.
Conditions in the heavily bombarded district are hellish. TV footage showed heavy snow and freezing weather, with residents lacking electricity or fuel for heating. There is also a shortage of food and medical supplies.
Barely a building has escaped damage from artillery shelling and many are pock-marked with bullet holes.