The 29-year-old was then taken to United's training ground at 9am to meet his new team-mates and sign the astonishing £250,000-a-week deal that will give him parity at the club with Rooney.
Van Persie then trained with his new club and is expected to go straight in to the team for the season's opener at Everton on Monday.
Sir Alex Ferguson said: 'Robin is a world-class striker with a proven record in England and in European football.
'His talents need no introduction to our fans – he has scored a number of goals against us in some classic battles with his former club. His movement, finishing and all-round ability are outstanding.
He later told MUTV: 'The boy wanted to come. He turned down various clubs. If he hadn't told Arsenal he wanted to go to Manchester United, the transfer wouldn't have happened.'
Ferguson admitted he thought it would be impossible to get Van Persie to sign, but had to make an attempt when the striker did not sign a new contract with the north London club.
Deadly: Van Persie was all smiles alongside Wayne Rooney in Friday's training session
Changing times: Van Persie is paraded inside Old Trafford after sealing his £24m switch
Delight: Van Persie was all smiles as he was shown off ahead of his press conference at Old Trafford
'It has given everyone a lift,' said Ferguson. 'I have a complication to my life (selection). I don't know how I managed in 1999.
'They can gel together. Robin's best position is furthest up the pitch. The most important thing is to win what we want to win. These players can help us to do that.'
At the press conference, Ferguson added: 'We never thought we could get Van Persie. If you go back six months ago, I couldn't see us getting him.
'I thought Arsenal are not going to let him go. When I read he had refused a new contract, that is when we acted. It has been a long haul.'
Even so, it took a personal intervention from Ferguson to get the deal moving last week after it had apparently stalled permanently.
'I can't elaborate but it was amicable,' said the Scot. 'Arsene knew the boy wanted to leave. He knew he wanted to join us. That made it a bit easier but not in terms of trying to reduce the fee.
'He (Wenger) could run a poker school in Govan. He got a great price but we are also happy the matter is concluded. From the starting position when we first started negotiating, Arsene has done well.'
Ferguson revealed he was still looking at a new signing for 'one more position' but 'only if a certain player came available'.
Van Persie's old Arsenal team-mate Cesc Fabregas tweeted: 'As a friend and team mate of mine for the last 8 years i want to wish good luck to @Persie_Official and his new adventure at Man United.'
An Arsenal statement read: 'Arsenal Football Club can confirm that Robin van Persie has now completed a transfer to Manchester United after terms were agreed between the clubs.
'This ends Robin’s eight-year association with Arsenal, after joining the Gunners from Dutch side Feyenoord in May 2004.
Pairing: Van Persie speaks at his Friday afternoon press conference as he sits next to Ferguson
Putting it all on red: Van Persie and Ferguson smile for the cameras at Old Trafford
'During his time with Arsenal, Van Persie made a total of 278 appearances for the Club, scoring 132 goals, including 37 from his 48 appearances last season.
'His fantastic performances during the 2011/12 campaign resulted in the PFA (Professional Footballers’ Association) and FWA (Football Writers’ Association) Player of the Year awards, together with the Premier League Golden Boot.
'Van Persie also became a regular in the Netherlands national team during his time with Arsenal, making 68 appearances to date.
'Everyone at Arsenal would like to thank Robin for his contribution during his time with the club.'
United fought off competition from Manchester City and Juventus to bring the Dutch striker to Old Trafford and hope he will be able to feature against Everton on Monday.
On Thursday, Ferguson claimed United will possess arguably Europe's most fearsome strike force when van Persie arrives.
Ferguson has spoken about the new-look attacking options of Van Persie, Wayne Rooney, Danny Welbeck and Javier Hernandez, and the comparisons with the 1999 set of Andy Cole, Dwight Yorke, Teddy Sheringham and Ole Gunnar Solskjaer.
Watching on: David Gill, agent Kees Vos and Van Persie's wife Bouchra at the press conference
Ferguson said: 'They (Wayne Rooney and Robin van Persie) are two fantastic players and it will be great to have both of them. It gives us more strength and more combinations up front.
'In 1999 I had Dwight Yorke, Andy Cole, Teddy Sheringham and Ole Gunnar Solskjaer, the four best strikers in Europe.
who will believe that this season he will get inj?
