Ramadi's mayor, Ibrahim al-Osaj, announced on Sunday that the returning families must go through security checks, adding nearly 12,000 families have returned since late last month.
He said the families are only allowed to return to the areas that have been cleared of the landmines and other explosives that Daesh planted before leaving.
Osaj added that seven neighborhoods of Ramadi are still out of bounds to civilians as they are still contaminated with mines and explosives or have been "totally ruined."
Ramadi is the capital of Iraq's western province of Anbar and is about 110 kilometers (68 miles) west of the capital Baghdad,
He said local authorities have fixed the water supply network in around 80 percent of the city, restored ten schools and accommodated those families that cannot use their old houses in 600 caravans.
Ramadi, which had fallen to Daesh last May, was liberated in December 2015.
The northern and western parts of Iraq have been plagued by violence ever since Daesh militants began a coordinated campaign in Iraqi territory in June 2014.
More than three million people have been forced to flee their homes in Iraq since January 2014, according to the United Nations.
The Iraqi army and volunteer Hashd al-Shaabi units have joined forces to take back territories from militants.
