Iraqi officials said the IS group had used laboratories in the university complex to make chemical weapons.
The head of the country`s counter-terrorism operations said retaking the area was a significant victory.
"This great scientific and cultural building was liberated by the heroes," Lt Gen Talib Shaghati, said. "The liberation of the University of Mosul means much, given its cultural, social and human symbolism."
Elite troops had entered the compound on Friday as part of a major push into new territory.
Iraqi military officials claim they now control a large majority of the city`s eastern half.
They also control three of the five key bridges crossing the river Tigris, which divides Mosul in two.
The bridges were targeted by coalition air strikes in October with the aim of limiting the ability of IS to resupply or reinforce their positions in the east.
The campaign began in October, but got off to a slow start in the face of tough IS defence and counter-attacks.
But significant gains along the river may open up western Mosul, which is still under IS control, to Iraqi forces seeking to advance.
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