The 22 year old spent most of the 2019-20 League One title-winning season on loan with the Sky Blues.
"We are delighted to welcome Callum back," said City boss Mark Robins.
"He has been one of our main transfer targets as we prepare for the Championship campaign, and we're very pleased to have fought off competition from other clubs to secure his signature.
"We know what great attributes Callum has and the quality he can bring to the side," added Robins.
"He is a player who is continuing to develop as a footballer. A popular member of the squad, and I know fans will welcome his arrival."