The Dutchman, 20, has joined Werder Bremen on a season-long loan deal.
Speaking to the club's website, Solskjaer said: "We are pleased with the progress Tahith has made since he stepped up from the Academy and are looking forward to continuing to develop his talent.
"He has great potential; given his age, ability and work-ethic, we can see that he has a bright future at Manchester United."
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