"Zero hour for the liberation of Fallujah has arrived. The moment of great victory has drawn near and Daesh has no choice but to flee," Iraqi Prime Minister Haider al-Abadi said on his official Twitter feed, using an Arabic acronym for the jihadist group.
He said the offensive would be conducted by the army, police, counterterrorism forces, local tribal fighters, and a coalition of mostly Shiite Muslim militias.
The US-led coalition that has bombed Islamic State in Iraq and neighbouring Syria for nearly two years was expected to provide air support.