Ramadi governor Hameed Dulaymi said on Sunday that the displaced families moved backed to areas that have been cleared of explosives.
They will use electricity generators as the public grid was not repaired and water from Euphrates river will be pumped to their houses, he said.
Ramadi, the provincial capital of Anbar, was liberated in December, almost one year after it fell into the hands of ISIS.
Also on Sunday, an Iraqi military official said that some 29 senior ISIS members had been killed in two airstrikes in Anbar province, al-Forat news agency reported.
Iraqi warplanes targeted two separate ISIS gatherings in al-Ghaem and Raweh towns. A number of ISIS militants were also injured in the attacks.
The liberation of Ramadi marked one of the most significant victories for Iraq’s armed forces since ISIS Takfiris seized swathes of the Iraqi land in June 2014.
Majority of Ramadi residents fled the fighting and took shelter in camps west of the Iraqi capital, Baghdad.
The militants have been committing crimes against all ethnic and religious communities in Iraq, including Shias, Sunnis, Kurds and Christians.
The Iraqi army and volunteer fighters have been engaged in operations to liberate militant-held regions.
The UN Assistance Mission for Iraq (UNAMI) said on Friday that armed clashes and violence killed 1,119 people and injured 1,561 others in Iraq in March, up from 670 deaths and 1,290 injuries in February.
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