Smoke covered parts of the Old City, rocked by air strikes and artillery salvos through the morning.
The Iraqi military remains engaged in a wide-ranging campaign - which began last October - to recapture the entire city of Mosul, which IS overran in mid-2014.
Authorities are planning a week of nationwide celebrations following the expected win, according to a government statement, and prime minister Haider al-Abadi is to visit Mosul to formally declare victory.
After eight months of grueling battles to retake Mosul, the dense west Mosul neighborhood is IS' last stand in Iraq's second-largest city.
The seizure of the almost 850-year-old Grand al-Nuri Mosque - from where Islamic State proclaimed the caliphate almost three years ago to the day - is a huge symbolic victory.
With Mosul gone, the group's territory in Iraq will be limited to a few areas west and south of the city where some tens of thousands of civilians live.
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"Their fictitious state has fallen", an Iraqi military spokesman, Brigadier General Yahya Rasool, told state TV.
Iraqi forces took control of the al-Nuri mosque in central Mosul, historically one of Islam's most iconic sites, from Daesh towards the end of June.
Isis has unleashed a wave of female suicide bombers targeting enemy troops and civilians as it clings on to its last remaining patch of Iraqi soil. On Sunday, a bomber in women's clothing killed 14 people at a camp for displaced residents in Anbar province, a provincial official said. These attributes drew to it young recruits even from Europe and the United States, not to say Muslim countries and India, who responded to its ideological call of returning to the roots of Islam. "They killed nine people and they kidnapped around 30", said Nour, who had spoken to fleeing villagers.
This frame grab from video released on Tuesday, July 4, 2017, and provided by Furat FM, a Syrian Kurdish activist-run media group, shows smoke rising from the Old City of Raqqa following heavy bombing as US -backed Syrian Democratic Forces (SDF) fighters advance toward the center of Raqqa, Syria.
The battles in the Old City's maze of narrow alleyways is fought house-by-house in streets packed with civilians and planted with multiple explosive devices by the militants, who are also using drones and suicide bombings.
But IS still controlled areas closer to the Syrian border and carried out attacks in government-held territory.