Van Persie is due to undergo a medical in Manchester tomorrow after an agreement was thrashed out by senior figures at Old Trafford and the Emirates Stadium.
United have beaten off competition from Manchester City and Juventus to sign last season’s double Footballer of the Year.
The 29 year-old, who becomes the first player to leave Arsenal for Manchester United since Viv Anderson, in the 1980s has been the centre of the summer’s most high-profile transfer saga after going public with his refusal to sign a new contract at the Emirates last month.
Talks between United and Arsenal are understood to have progressed well on Wednesday, with the final stage being a discussion about add-ons to take the deal to a final figure of £22m.
United manager Sir Alex Ferguson had insisted that the Old Trafford club would not pay in excess of £15m for Van Persie, with Arsenal holding out for £25m.