The 46-year-old former defender, who was previously coach at Austria's Sturm Graz, takes over from caretaker Neil Redfearn at the Yorkshire club who won the English title in 1992 but were relegated from the Premier League a decade ago.
Leeds, owned by Italian Massimo Cellino, sacked manager David Hockaday in August after only six games in charge at Elland Road.
"I don't know (why I've chosen him). The coaches are like watermelons. You find out about them when you open them," Cellino, who also described Milanic as a 'very cool guy', told Sky Sports News.
"His particular qualities? He's good looking, what can I tell you?
"He was a very good counter-attacking defender with Partizan Belgrade and Sturm Graz, and a good coach with Maribor for four years and took the club to the Champions League and Europa League, and he made it good as player and coach and he likes the Premier League," added the Italian.
Cellino, who bought Leeds in April, dismissed 36 managers during 22 years as owner of Italian club Cagliari.
(Reporting by Alan Baldwin, editing by Toby Davis)
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