The revelation was made on United's website on Wednesday following intense negotiations between the two clubs in recent days.
The short statement read:
"Manchester United is pleased to announce it has reached agreement with Arsenal Football Club for the transfer of Robin Van Persie.
"The deal is subject to a medical and the agreement of personal terms. A further announcement will be made in due course."
Although Van Persie has had plenty of injury problems during his career, after an almost clean bill of health in the past year, it is not anticipated that the medical will present a significant hurdle. It is also highly unlikely that United will have pushed so hard to strike a deal with Arsenal had they not already had a basic understanding of the personal terms that would be agreeable to Van Persie.
In a hectic period for United's staff, the club is also expected to announce the signing of Chilean Angelo Henriquez in the next few days. The 18-year-old forward was in Manchester on Tuesday to complete a medical ahead of a proposed £3.5 million move from Universidad de Chile
Henriquez, who has been tracked by United's scouts for some time, said he was delighted that the transfer was finally happening.
"I am super happy to get to Manchester United. I'm fulfilling a dream," he said, according to the Daily Mail.
"I am going where I wanted. You look on television and see the outstanding players, scoring spectacular goals. I cannot waste this opportunity.
"It is not clear what will happen with my future. I want to play in the first team of Manchester United. That's my first thought.
"If they decide to send me on loan, I would prefer to continue at Universidad, although I will do whatever United deem appropriate
The impending arrivals of both Van Persie and Henriquez make it highly unlikely that United will pursue their reported interest in Robert Lewandowski this summer. The Poland international had been linked with a move to Old Trafford after scoring the goals to lead Borussia Dortmund to the German league and cup double last season.
But, Lewandowski has said that he is happy to remain in Dortmund for the time being.
"The rumors about me and other teams are not of any interest to me," he said, according to Sky Sports.
"I have two years on my deal at Borussia Dortmund and I am still a player at this club."
Meanwhile, Dortmund manager Jurgen Klopp has claimed that Lewandowski's agents having been the ones talking up a move.
"Robert is an exceptional player. He will always be in my squads. Unfortunately his agents will not, there is no doubt about that."
With the club yet to add a central midfielder this summer, United could still move to bolster a department that has often looked under-strength in recent times.
A reported target of United, Moussa Dembele has been discussing his future while on international duty with Belgium.
The Fulham man, who has flourished in a midfield role after previously being deployed up front, claims that Real Madrid have contacted his agent about a move.
"I do not know [if I will leave]," he said, according to the Guardian. "Actually I can say nothing about it.
"There was contact between Real and my agent. They wanted information, but that was it. Everything is still."