Wilson is ready to grab "a real opportunity", according to Aberdeen manager Derek McInnes as the striker arrived on loan.
The Dons say the 22-year-old former England Under-21 international was "sought after by a number of other clubs" before his season-long deal.
"He is a player I feel will very quickly become an important member of the squad," McInnes told Dons' website.
"He is a real quality player who I think will suit the way we play."
Wilson first hit the headlines when he scored twice on his United debut in a 3-1 win over Hull City as an 18-year-old.
But he has since only made six starts - and 14 substitute appearances, scoring twice more - for the English Premier League club.
"Having spoken to him, I think he sees this move as a real opportunity for him," McInnes said.
"There were other clubs interested in taking James, but he feels this is the right place for him to continue his development."
Wilson, whose progress was hampered by a serious knee injury while on loan to Derby, is contracted to United until summer 2019 with an option to extend that by a further year.