Milanic arrives at Elland Road from Austrian side Sturm Graz, succeeding Dave Hockaday, who was sacked by Leeds owner Massimo Cellino on August 28 after just six games.
The 46-year-old - winner of four Slovenian Championships during his time with Maribor - has brought assistant Novica Nikcevic with him from Sturm, with caretaker boss Neil Redfearn taking over the academy team after winning three of his four games in charge.
"Coaches are like water melons, you only find out how good they are when you open them," declared Cellino on Sky Sports News. "But he looks good and we needed a coach with a bit more experience.
"He was a very good centre-back with Partizan Belgrade and he was a good coach for Maribor for four years, taking them into the Champions League and the Europa League.
"He's not the type to get too excited about coming here, he's a very cool guy. He doesn't talk much and is pretty pragmatic, but I like him and it's very encouraging for the future of Leeds."
Milanic's first game in charge will be at Brentford on Saturday and he takes over with Leeds in 12th place in the Championship table, five points adrift of leaders Nottingham Forest and just two points below the play-off places.