The operation "is done and the city is fully liberated," Abdul-Wahad Saadi said.
"We announce from this place in central Golan district that it has been cleaned by the counter terrorism service and we convey the good news to the Iraqi people that the battle of Fallujah is over," Lieutenant General Abdul Wahab al-Saidi told state TV.
Earlier in the day Lieutenant General of the Iraqi army told AFP:
"I can say that more than 80 percent [of the city] is controlled by our forces,"
Fallujah, located some 42 miles west of the Iraqi capital Baghdad, is one of the largest cities in the Anbar province. Daesh has been in control of the city since 2014.