The Slovenian had been heavily linked to the position and he has signed a two-year deal with the club.
He will be joined at the Whites by Novica Nikcevic, who was his assistant at Sturm Graz.
"Yes, we agreed a two-year deal," Leeds owner Massimo Cellino told Sky Sports News. "He's just arrived today. We've been waiting for him about 15 days.
"I don't know [why I've chosen him]. The coaches are like watermelons. You find out about them when you open them.
"His particular qualities? He's good looking, what can I tell you?"
Milanic was in charge of Graz for a season, following five years at previous club Maribor.