The 46-year-old was appointed on Tuesday after resigning from Austrian club Sturm Graz. He had previously won nine trophies in five years for Maribor in his homeland.
He becomes the third manager in a year under Leeds' impatient Italian owner Massimo Cellini, who dismissed more than 30 of them in his 22 years in charge of Italian club Cagliari.
Leeds are 11th in the English second tier having won four of their eight league games.
This week Cellini likened coaches to water melons, saying "You find out about them when you open them".
Milanic's predecessor, Dave Hockaday, who took over from Brian McDermott at the start of the season, lasted six games before being sacked a month ago.
However, Milanic said on Wednesday that the team's current unbeaten run of four matches gave him cause for optimism.
"I know that the team is now in a good shape and this is a very good moment for the team," he said.
"I know that it will be very tough but the team has to move forward. The team needs to continue the form like the last few games.
"This is a very special thing for me to be the head coach of such a big club with great tradition and great fans. For me this is a great opportunity to improve myself and also the team.
"Leeds is one of the most traditional clubs in England and they have had great players in their history."
Leeds had always employed managers from England or Scotland -- the exception being David O'Leary, the former Arsenal and Ireland defender -- who was boss at Elland Road from 1998-2002.
Champions of England in 1969, 1974 and 1992, Leeds were beaten finalists in the 1975 European Cup and Champions League semi-finalists in 2001.
But they were relegated from the Premier League amid a financial crisis three years later and from 2007 spent three seasons in League One (third tier) until returning to the Championship.
(Writing by Steve Tongue, editing by Mike Collett and Ken Ferris)
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