Milanic, 46, has secured his release from Graz and is due to travel to England tomorrow to finalise terms with United owner Massimo Cellino.
The Slovenian was lined up for the job at Leeds at the start of this week and he will assume control at Elland Road after taking charge of Graz for the final time against SV Josko Ried this evening.
Milanic is understood to have exercised a clause allowing him to buy his way out of a three-year deal with Graz and he should put pen to paper on a contract at Leeds over the weekend.
Leeds have been without a head coach since sacking David Hockaday on August 28 and Milanic came into the reckoning after Cellino failed to lure Oscar Garcia to the club at the start of the international break.
Academy manager Neil Redfearn will take charge of today’s Yorkshire derby against Huddersfield Town - his fourth game in charge - before making way for Milanic to assume control of the senior squad early next week.
Milanic has been head coach of Sturm Graz for the past year, enduring a mixed run of results which saw the club finish in a mid-table position in the Austrian Bundesliga last season.
He previously enjoyed a highly successful spell in charge of Slovenian side Maribor, winning nine domestic trophies during five seasons as boss.