The Red Devils have secured the services of the 17-year-old for an undisclosed fee and the player will stay with his current club for another season before making the move to England.
Milinkovic has represented the Serbian Under-17 squad on six occasions as they narrowly missed out on qualification for the UEFA Under-17 Championship.
The goalkeeper will follow in the footsteps of fellow countrymen Nemanja Vidic and Zoran Tosic if he eventually makes a first-team appearance for the Manchester club.
The arrival of Milinkovic marks the club’s first bit of transfer business since the recent sacking of manager David Moyes.
Netherlands head coach Louis Van Gaal has been tipped to be appointed to the Old Trafford hot-seat early next week.