* Inzaghi shown door after poor season
* Mihajlovic becomes Milan's fourth coach in 18 months (Adds detail, quotes)
MILAN, June 16 (Reuters) - Sinisa Mihajlovic became AC Milan's fourth coach in 18 months on Tuesday after Filippo Inzaghi was sacked following yet another disappointing season for the seven-times European champions.
Former Milan striker Inzaghi, 41, had been in charge for one season, leading them to a modest 10th as they failed to qualify for Europe for the second consecutive season.
Milan said Mihajlovic had signed a two-year contract.
The Serb, who took charge of Sampdoria in November 2013 when they were second from bottom in Serie A, leading them to a 12th-place finish last season and seventh this term, faces a huge task turning round Milan's fortunes.