The former Ajax midfielder joins on a four-year contract with the option to extend for a further year.
"It feels very good and I am very excited to start. I am very happy to be here," Blind told MUTV.
"It has been very busy. Everything was going so fast so I didn't really have time to think about it all, but as I said I'm really happy to be here.
"United are one of the biggest clubs in the world. If you look at their history they have won a lot of cups and they have had players here for their whole career, like Ryan Giggs and Paul Scholes. Those are players everyone knows about and I am a big fan of them. It's now a dream come true to play for Manchester United and I'm very happy that I have this chance."
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