U.S.-led and senior Iraqi military officers said the troops entered the school grounds in the early morning hours and by afternoon had taken control of the neighborhood on the northeast edge of the compound and technical institute of the campus.
By nightfall, Iraqi forces had also taken control of the Nineveh governorate and council buildings, according to a statement from the U.S.-led coalition.
"We congratulate the Iraqi Security Forces on their continued progress in Eastern Mosul," said Army Col. John Dorrian. "Work still needs to be done but ISIL's days in Mosul are quickly coming to an end." Dorrian is a spokesman for the U.S.-led anti-IS coalition.
There was thick dark smoke at the complex and by afternoon, the fighting became intense with sniper and mortar fire targeting the Iraqi forces.
This latest push comes a day after the Iraqi army north of the city linked up with troops pushing in from the eastern outskirts. ISIS still controls the western part of Mosul.
The coalition told the Associated Press that ISIS "warped the purpose of a beloved institution of higher learning when they used the university for military purposes."
"The entire university has been burned," said a student named Muhammad. "I think it will take at least two or three years to rebuild," he added.
Syrian TV said three people were killed and nine wounded in ISIS rocket attacks in several city neighborhoods.
Activists and Syrian warplanes were in the fighting as well.
ISIS seized large areas in Iraq and Syria in 2014, establishing an Islamic caliphate, which is the goal of Islam globally, but they will never admit it. Now they have lost a significant amount of territory in recent months.