The 31-year-old, who missed a large part of last season with knee ligament damage, has agreed a two-year deal at the Emirates Stadium after nine years at Old Trafford.
With his contract set to expire next season Silvestre had been linked with a move to Bordeaux and Manchester City during the summer - but has opted to move to north London.
Silvestre had fallen down the pecking order at United with Nemanja Vidic and Rio Ferdinand becoming Sir Alex Ferguson's first-choice partnership at the heart of the defence.
Wes Brown and John O'Shea can also provide cover in the centre and have recently agreed new deals at the club, while Patrice Evra has made the left-back spot his own.
And with his contract set to expire in 2009 Ferguson has allowed Silvestre - who is the first player to leave United for Arsenal since Brian Kidd 34 years ago - to join one of their major Premier League rivals.
What is equally surprising though is the fact that Wenger has handed Silvestre, who has a recent history of injury problems, a two-year contract.
It represents a change in policy for the Arsenal boss who has previously been reluctant to offer players over 30 - including the likes of Robert Pires, Jens Lehmann and Dennis Bergkamp - anything more than a one-year deal.
Arsenal, though, are short on experience and Wenger cited Silvestre's ability to fulfil several defensive positions as the two factors behind the deal.
Wenger said: "We have a strong squad but a young squad and Mikael's versatility, experience and calibre will provide the extra depth we need to reinforce our challenge for honours this season.
"His defensive adaptability will serve us well and it's a big plus that Mikael has top-level experience and a great understanding of football in the Premier League."
Ferguson signed Silvestre from Inter Milan in 1999 after he began his career with Rennes who he left for the San Siro in 1998.
Silvestre enjoyed considerable success with the Red Devils and won four Premier League titles, an FA Cup winner's medal and a League Cup winner's medal in his 361 appearances with the club.
But his final season at United was hampered by a knee ligament injury sustained against Everton in September 2007 which restricted him to just six competitive appearances.
Silvestre, who has also won 40 caps for France and was part of the squad which reached the World Cup final in 2006, is looking forward to a new phase in his career.
"I've spent a large part of my career at United, the last nine years, and I'll remember that time fondly but feel I'm ready for a new challenge," said Silvestre who has been handed the number 18 shirt.
"Arsenal is known for playing technical and skilful football, and has a young but experienced squad.
"I'm really excited about this next stage of my career, hopefully playing my part in helping the club to new successes."
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