Sporadic bursts of gunfire could still be heard on Sunday, and plumes of smoke rose into the sky.
Thirty IS militants were killed as they attempted to escape the advance of the Iraqi forces by throwing themselves in the River Tigris, state media said.
The government announced the full "liberation" of eastern Mosul in January, but the west of the city, with its narrow, winding streets, has presented a more difficult challenge.
Some 900,000 people have been displaced from the city since 2014 - about half the the pre-war population - aid organisations say.
The Islamic State group has lost large parts of the territory it once controlled in Iraq since the regional offensive began.
But the fall of Mosul does not mean the end of IS in the country, as it still has territory areas elsewhere and is able to carry out bombings in government-held areas.
French President Emmanuel Macron was among the first to hail the victory of Iraqi forces in Mosul on Sunday, praising the fighters - including French troops in the coalition - who had made it possible.
Analysis: Victory at a terrible cost
By Sebastian Usher, BBC Arab affairs editor
The army has avenged its humiliating defeat by the militants in Mosul three years ago. But victory has come at a terrible cost.
Thousands of civilians have been killed. Much of Mosul has been destroyed.
And the dangers posed by the Islamic State group are not at end.
The militants will go underground and they may well look to make hit-and-run attacks in classic guerrilla style - in Mosul and many other places.