The highly-rated prospect is believed to have been on trial at Old Trafford in recent weeks, with United confirming on Saturday that he has joined the club.
Milinkovic is a Serbian Under-17 international and will remain with Vojvodina next season as United clearly look to the future in terms of goalkeeping options.
Provided he can secure himself a first-team place at United, he would become the third Serb to play for the club following departing captain Nemanja Vidic, who will join Inter this close-season, and Zoran Tosic, now at CSKA Moscow.
Vidic made 300 appearances during his eight-year spell, while Tosic made just five.
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