Last season’s top scorer and player of the year will complete a move to Old Trafford in the next 48 hours and could make his United debut in their opening match of the season on Monday at Everton.
The Holland forward, who scored 44 in 57 games last season, is set to earn more than £200,000 a week, having rejected Arsenal’s offer of a new contract with a pay rise to around £120,000 per week.
Van Persie gave furious Gunners chiefs little choice but to sell by declaring last month that, with 12 months left on his deal, he would not sign new terms because he had lost faith the club’s direction.
Italian champions Juventus and Premier League winners Manchester City also courted Van Persie, but he is understood to have made it clear that United, Arsenal’s one-time rivals, were his preferred destination.
Wenger drove a hard bargain in exchange for selling to United manager Sir Alex Ferguson, with whom he has endured an at times bitter relationship, rejecting lower bids and demanding £25m for the 29-year-old.
The Frenchman prepared for Van Persie’s departure by signing two forwards early in the close season, in versatile Germany star Lukas Podolski and French football’s top scorer last term, Olivier Giroud.
But the Arsenal boss will come under pressure to reinvest the proceeds of Van Persie’s sale in order to repair some of the morale damaged by the loss of the club’s star player to a club they aspire to challenge.
The deal represents a coup for United, seeking to recapture their title from big-spending neighbours City, although the fee is a gamble given the Dutchman’s history of injuries before last season.
The Gunners said in a statement: “Arsenal can confirm that terms have been agreed for the transfer of Robin van Persie to Manchester United. Van Persie will travel to Manchester on Thursday in order to agree personal terms and complete a medical.”