Inzaghi was dismissed one day after his side lost 4-0 at home to second-bottom Frosinone, leaving the seven-times Italian champions stuck in the relegation zone, with a performance described by club president Joey Saputo as "pitiful".
The 45-year-old ex-AC Milan and Italy forward, the eighth Serie A coaching victim of the season, has managed just two wins in 21 league games this term and none in the last 14 outings.
"The club sends its heartfelt thanks to Filippo Inzaghi for the work he carried out with professionalism and passion," said Bologna in a statement.
The 49-year-old Mihajlovic, who by coincidence also replaced Inzaghi at AC Milan in 2015, began his coaching career at Bologna in 2008-09 although he lasted only six months.
Since then, the Serb -- famous for scoring spectacular free kicks as a player -- has coached Catania, Fiorentina, Sampdoria, AC Milan and Torino in Serie A and Serbia's national team.
Mihajlovic, who has a contract until the end of the season with an option for another term, was sacked by Portuguese club Sporting in June after only nine days without having taken charge of a match.
He was appointed days before Sporting president Bruno de Carvalho was voted out of office and the new administration cancelled his contract.
Bologna, who won the last of their Serie A titles in 1964, are third from bottom of the standings with 14 points, one point above Frosinone but three adrift of the safety zone.
(Writing by Brian Homewood; Editing by Ken Ferris)
