The operation took four hours. ISIS continued to fire mortars at the airport from further inside the city after losing the ground to the army.
The jihadists have also entered a nearby military base amid further clashes, a military spokesman said.
Eastern Mosul was retaken last month.
Today’s advance brings the army within less than a mile of western Mosul, where the militants are expected to launch attacks from densely populated neighborhoods.
The assault began with air strikes by the US-led coalition before armored columns advanced to the airport’s perimeter.
Iraqi forces also came under fire from ISIS militants holed up inside airport buildings, reports said.
Foreign troops from the US-led coalition were with the attacking troops, officials told the Associated Press, without specifying their nationality.
According to reports, the airport’s runway has been destroyed by ISIS.
The airport and the al-Ghazlani base are on Mosul’s southern outskirts on the western side of the Tigris River.
Thousands of Iraqi troops, backed by artillery and air power, are involved in the assault to retake Mosul.
Leaflets warning residents of an imminent offensive were earlier dropped over western Mosul, where military officials say narrow winding streets could make retaking the area particularly difficult.
Although slightly smaller than the east, western Mosul is more densely populated and includes districts seen as pro-ISIS.
The UN has voiced concern about the welfare of civilians trapped in the city.
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