The appointment comes after Milanic took first-team training for the first time on Tuesday, with United set to officially unveil the former Maribor boss on Wednesday at a press conference.
Milanic left his head coach role at Austrian side Sturm Graz on Sunday and he will now sign a new two-year deal at Elland Road.
After sacking Dave Hockaday, Cellino turned Neil Redfearn who did sensationally well picking up 10 points from 12 during his tenure. Saturday's 3-0 win over Huddersfield proved once again the ability in the squad and Redfearn is set to play his part in a coaching team at Leeds.
Milanic's assistant at Sturm Graz, Novica Nikcevic will also join him at Elland Road as part of a new coaching setup.
During his time at Maribor, Milanic guided his side to four Slovenian league title and three cup wins but his new task will see his ability tested in a different way.
He has experience of managing in the Champions League and Europa League but United's form under Redfearn will certainly add to the pressure.
His first game will come against Brentford on Saturday with United also set to face Reading and Sheffield Wednesday next week.