"Manchester United is pleased to announce it has reached agreement with Arsenal Football Club for the transfer of Robin Van Persie," said a club statement.
"The deal is subject to a medical and the agreement of personal terms. A further announcement will be made in due course."
Van Persie stunned Arsenal manager Arsene Wenger when he declared immediately after Euro 2012 that he wanted to leave the north London team because he felt the club's ambitions did not match his own.
That came after a superb season where the forward scored 37 goals in all competitions, a tally that led him to being voted player of the year by both his fellow professionals in England and the country's Football Writers' Association.
Van Persie's announcement sparked interest from Premier League champions Manchester City, as well as Italian giants Juventus, but it is United manager Alex Ferguson who has won the race for the striker's coveted signature.
It is not expected either a medical or indeed personal terms will prove a barrier to the 29-year-old's move to Old Trafford.
No fee has been confirmed by either United or Arsenal, although it has been reported as around the £20million mark.
Provided the deal goes through smoothly, van Persie could make his United debut in their Premier League opener away to Everton on Monday.
The transfer is set to be the most expensive deal United have done since Dimitar Berbatov's club record £30.75m move from Tottenham in 2008.
Ferguson made van Persie one of his main pre-season targets, despite already having Wayne Rooney, Danny Welbeck and Javier Hernandez in his squad.
The veteran Scottish boss even went so far as speaking directly to Wenger in a bid to make sure the deal went through.
French boss Wenger did not want to sell prize asset van Persie to a rival Premier League club.
But, with supporters turning against their former favourite during a pre-season match with Cologne on Sunday and van Persie having just a year left on his Gunners contract, he clearly decided it was better to sell him for a large fee than see him leave for nothing in 12 months' time.
But with van Persie having followed former Arsenal stars Cesc Fabregas and Samir Nasri -- sold to Barcelona and Manchester City respectively last year -- out of the Emirates, questions will be asked about Arsenal's determination to end a seven-year trophy drought.