An official declaration of victory from the government is expected soon.
Iraqi forces, backed by US-led air strikes, have tried to retake the city since 17 October last year.
IS seized Mosul in June 2014 before sweeping across much of Iraq's Sunni Arab heartland and proclaiming a "caliphate" straddling Iraq and Syria.
But they have been losing ground over the past nine months, as government forces advance on their former Iraqi stronghold.
Kurdish Peshmerga fighters, Sunni Arab tribesmen and Shia militiamen, supported by US-led coalition warplanes and military advisers, have been involved in the battle.
On Saturday the jihadists were desperately holding out in a tiny area near the Old City. State television said troops had expected to take full control within hours.