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Milan will not compete in Europe next season after finishing down in midtable alongside city rivals Inter, spelling the end for Inzaghi, who failed to lift the club out of the gloom after taking over from former team-mate Clarence Seedorf last season.
"AC Milan announces that it has sacked first team coach Filippo Inzaghi, whom it thanks for the work done," the Serie A giants said in a statement.
Former Sampdoria coach Mihajlovic has signed a two-year deal with Milan, the seven-time European champions added.
Inzaghi, nicknamed Superpippo, made his name as a player with Milan, scoring 126 goals in 300 games and winning 10 titles including the Champions League twice.
But the 41-year-old was widely seen as having been out of his depth since stepping up from coaching the youth team to replace Seedorf in June 2014.
Milan's billionaire owner Silvio Berlusconi had admitted to having "different visions" to Inzaghi on the club.
The media tycoon, who is seeking outside investors to help him revive the club's fortunes, said Inzaghi had ignored his request for players emerging from the club's academy to be given a chance.
Milan went on to finish 10th in this season's Serie A, their worst season since Berlusconi acquired the club three decades ago.
