The Netherlands international, who has been linked with the likes of Manchester City and Juventus in recent months, completed a medical last night before thrashing out the last few details of what is thought to be a £24m transfer.
"It's an honour to sign for Manchester United," Van Persie told the club's official website.
"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."
Red Devils boss Sir Alex Ferguson added: "Robin is a world-class striker with a proven record in England and in European football.
"His talents need no introduction to our fans, he has scored a number of goals against us in some classic battles with his former club. His movement, finishing and all-round ability are outstanding."
Van Persie's transfer was completed before midday today, which means that the 29-year-old is eligible to make his United debut against Everton on Monday night.