The club confirmed the acquisition of the 29-year-old striker on Friday morning after the Netherlands international completed a medical on Thursday night.
Van Persie will go straight into the United squad for their Premier League opener away to Everton on Monday night.
"Robin is a world-class striker with a proven record in England and in European football," manager Sir Alex Ferguson said in a press conference.
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The new Red Devils striker, who scored 30 top flight goals last season, spoke of his delight in putting pen to paper at Old Trafford and is ready to kick off the campaign with his new club.
"It's an honour to sign for Manchester United," said Van Persie.
"I am looking forward to following in the footsteps of so many great strikers, bringing my experience and playing my part to help the team compete for the biggest trophies in the game. I can't wait to get started."