The Dutchman will arrive in Manchester on Thursday with the hope of sealing his £24million switch before the season starts on Saturday.
Arsenal had been keen to keep hold of last season’s top scorer int he Premier League, but have caved under pressure from the player, who released a statement last month expressing his desire to leave the club.
A statement on United’s website said: ‘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.’
Arsenal added their own statement, which read: ‘Arsenal Football Club 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 ahead of the proposed move.’
Speaking on French television, Arsene Wenger said: ‘It’s sad to lose a player of his quality. He had only one year left on his contract so we didn’t have the choice.’
The Gunners boss was then asked who he planned to replace the departing Dutchman with, to which he added: ‘We already signed [Lukas] Podolski and [Olivier] Giroud.’
The transfer represents the biggest deal United have done since Dimitar Berbatov’s club record £30.75m move from Tottenham in 2008.