The prolific attacker underwent a medical at the Old Trafford side on Thursday after both clubs had reached an agreement over a transfer fee on Wednesday,
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"Robin's transfer to Manchester United is fantastic not just for himself, but for Dutch football in general, too," Van Gaal was quoted as saying by Algemeen Dagblad.
"Robin followed his heart in this matter."
Van Gaal had some less positive news for Van Persie earlier this week when he told the forward that he is no longer first choice with Oranje as the former Bayern Munich coach prefers Klaas-Jan Huntelaar up front.
Netherlands lost their opening game of Van Gaal's reign 4-2 to near neighbours Belgium on Wednesday.