The Slovenian coach is leaving the Austrian outfit and will take Novica Nikcevic to Elland Road as assistant.
That Nikcevic is poised to also leave Sturm Graz was confirmed by the Austrian side's sporting director Gerhard Goldbrich.
The sporting director confirmed to Austrian outlet SportNet that the final deal for Milanic to join Leeds has not been signed off on yet, but added "however we assume that Darko Milanic and Novica Nikcevic will go to Leeds."
Milanic will succeed David Hockaday as Leeds boss, following the former Forest Green Rovers manager's sacking last month.