Leeds are currently 12th in the league table following four victories, one draw and two defeats.
During Milanic's official unveiling, the coach told reporters: "I'm very motivated and excited about the new job. I know that this is a very big club, a very traditional club with great supporters and they have very good quality in the team.
"They want to go in the future to the Premier League. I'm proud to be here. I have to improve the team, we have to improve in a lot of segments. I'll try to do my best."
Milanic spent one season at Austrian side SK Sturm Graz prior to his move to Leeds.