Arsenal accepted a £24 million offer from United last night.
The Sun says Van Persie, 29, who refused to sign a new deal at Arsenal, has been told he will be played at United as an out-and-out striker.
Wayne Rooney will operate in a free role behind him.
United will pay £15m cash up front with the fee rising to a guaranteed £22m. But, depending on other add-ons, Arsenal could still land £24m.