The Dutch international was delighted to sign for the Old Trafford club and said, "It's an honour to sign for Manchester United."
"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," Daily Mail quoted Van Persie, as saying.
Van Persie completed a medical in Manchester on Thursday and is likely to make his United debut against Everton on Monday night.
The Dutch star will earn a mammoth £250,000-a-week similar to United striker Wayne Rooney.
Van Persie is expected to train with his new teammates on Saturday and begin his new career on Monday against the Toffees at Goodison Park.
"Robin is a world-class striker with a proven record in England and in European football," Sir Alex Ferguson said.
"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," the United boss added.
Van Persie joined Arsenal eight years ago in May 2004 from Dutch side Feyenoord. During his time with Arsenal, Van Persie made a total of 278 appearances scoring 132 goals in which 37 out of 48 appearances came during the last season.