However, it was not clear yesterday whether the offer would come with sufficient guarantees for the safety of those trapped in the besieged area to satisfy aid agencies.
The government's announcement of the agreement came hours after rebels declared a new offensive in the northern province of Aleppo, in response to an escalated air assault by government forces trying to recapture territory and drive residents out of opposition-held areas.
President Bashar al Assad's forces have used a siege tactic to surround and try to starve out rebels holding strategic areas, a technique increasingly copied by rebels as well.
The siege of the old city of Homs has gone on for more than a year and activists say some 2500 people are now trapped inside the area struggling with hunger and malnourishment.
They represent only a small fraction of besieged Syrians across the country in desperate need of aid.
The Syrian foreign ministry said in a statement: "The agreement will allow innocent civilians surrounded in the neighbourhoods of Old Homs - among them women and children, the wounded and the elderly - an opportunity to leave as soon as the necessary arrangements are made, in addition to offering them humanitarian aid.
"It will also allow in aid to civilians who choose to stay inside the old city."
Delegates from Syria's warring sides met face to face for the first time at the Geneva 2 peace conference last week and were unable to agree anything, even a humanitarian deal for Homs that diplomats had hoped could be a relatively easy first step.
A second round of talks is scheduled for next week.
The government statement did not elaborate on who would be considered "innocent".
Rebels have rejected similar offers to evacuate women and children in the past because of fear for the fate of any men left behind. Dozens of men disappeared after a similar deal was reached in Mouadamiya, west of Damascus.
An official at Syria's Defence Ministry said rebel fighters were keeping civilians in the area as human shields.
He added: "As for civilians, we are not holding them up or refusing them humanitarian aid but the terrorists are the problem.
"Terrorists are claiming there are only civilians in the Old City who need humanitarian aid. In fact, it's terrorists who are mainly there, including foreign militants, using small groups of civilians held as hostages."
One report said the evacuation of civilians and the arrival of humanitarian aid was due to start today.
Meanwhile, the head of the international chemical weapons mission in Syria has told the UN Security Council the looming deadline for the elimination of the government's toxic arsenal was vital.
The remarks were made by Sigrid Kaag, head of the joint mission of the UN and the Organisation for the Prohibition of Chemical Weapons (OPCW) that is overseeing the destruction of Syria's chemical arsenal.
She said: "With the deadline on the horizon, the time for action is now."