United announced in May that a move had been agreed and the Serbia U19 international would be loaned back to his current side before arriving in Manchester after the Serbian season.
Vojvodina club president Zoran Scepanovic said: "After lengthy talks that have taken place over the past month, we have finally completed negotiations on Monday and we can officially inform the public that our young and promising goalkeeper has joined Manchester United.
"He will remain in Vojvodina for the next year, where he will be under the supervision of our experts and coaches from the English football giants, while continuing to train and perform in the jersey of his home club.
"This is an opportunity to thank everyone who participated in the realisation of this transfer. Can I point out Manchester United's very correct attitude."