The agreement with Syria's government also clears the way for the delivery of essential lifesaving supplies for about 2,500 civilians, UN spokesman Farhan Haq told reporters, citing comments from Valerie Amos, the UN Under-Secretary-General for Humanitarian Affairs and Emergency Relief.
Rebel-held Old City areas of central Homs have come under near-daily shelling ever since the army blockaded them in June 2012.
According to Syria's state news agency, "authorities will implement the deal by providing the necessary humanitarian assistance, including food, shelter and medical aid for innocent civilians who leave" the besieged districts.
"We need to see unhindered continuous and safe access for humanitarian workers to the millions of people trapped," Haq, quoting Amos, added.
If the Homs agreement enters into force it would be the first such gesture by President Bashar al-Assad's regime since negotiations with the Syrian opposition and involving world powers were held in Geneva last month.
An agreement to allow civilians to leave Homs was announced in Geneva, but the Syrian government and the opposition later accused each other of blocking the plan.