Van Persie's arrival at Old Trafford will limit Welbeck's opportunities in the first team as the Dutchman and Wayne Rooney will most likely form Sir Alex's first choice strike partnership.
However, the United manager believes 29-year-old van Persie can pass on his experience to the younger players in a similar way to how Eric Cantona nurtured his young side 20 years ago.
"You can always learn from great players," he told the club's official website.
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"Remember what Cantona did for all the young players when he arrived? He was a tremendous teacher for them.
"Danny will learn from playing with Robin, [Wayne] Rooney and Chicharito. I think we have a great combination of strikers now and that's encouraged me."
Sir Alex added: "I saw his interview and it was very refreshing. He started talking about scoring more goals – I hope he's right!
"At 21 he's a young boy. He's still growing and has niggles, but he’s going to be a big boy. He won't play every week but when he's 23 or 24 he’ll be a fantastic player.
Welbeck made his breakthrough last season, playing a prominent role in Manchester United's title challenge and England's Euro 2012 campaign, after a successful loan spell at Sunderland the year before.