The Serb, who resurrected Sampdoria during one-and-a-half seasons with the Genoa club in his previous job, became Milan's fourth coach in just over 18 months as he was presented alongside club president Silvio Berlusconi.
Milan have endured a miserable past two seasons, missing out on European football both times, and the club leadership has looked rudderless.
"The only way I can win over the fans is hard work," Mihajlovic told reporters.
"Milan have always been a side to be feared and I want that Milan side back. I want my Milan team to instil fear in other teams.
"We will be like our motto, a team of devils, red like fire and black like the fear we will instil into our opponents. I am convinced that we can achieve good things this season."
Unlike the previous two incumbents Clarence Seedorf and Filippo Inzaghi, Mihajlovic has no previous connections with Milan.
The 46-year-old played for AS Roma, Sampdoria, Lazio and Inter Milan and has coached Bologna, Catania, Fiorentina and Sampdoria.
"This is a club that has an enormous history. I am not part of the Milan history, so I thank the club for the faith in me," he said.
"It has been a couple of difficult seasons for Milan and I want to take them back to the top.
"The club are working very hard on the transfer market. The president is doing everything he can to give me everything I ask for.
"There isn't another ambitious project as this in Italy right now. You have to aim high, but the name is not enough. You have to respect it."
(Writing by Brian Homewood in Berne, editing by Ed Osmond)
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