Welbeck considered leaving United after becoming frustrated at being played out of position under David Moyes.
But with the Scot gone, Welbeck now has a chance to prove himself under Van Gaal, and the United forward is looking forward to working under the former Barcelona, Ajax and Bayern Munich coach next season.
"I heard the news (about Van Gaal's appointment) and I am happy," said Welbeck, who scored 11 times for United last year after starting just 24 matches in all competitions.
"He is a great man, a great manager.
"Looking at his CV tells you he has managed at some big clubs."
Current Holland coach Van Gaal was named United boss on Monday, a month after Moyes was sacked.
The 62-year-old, who will be assisted by Ryan Giggs, will take over at Old Trafford when Holland's World Cup campaign ends.
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