The 31-year-old joined United in September 1999 and had one year left on his contract at Old Trafford, but has now signed a two-year deal at Arsenal.
He made 249 Premier League appearances in nearly nine years with United.
Silvestre, also linked with Manchester City and Bordeaux, missed most of last season with a knee ligament injury, but returned to action in April.
"I've spent a large part of my career at United and I'll remember that time fondly but feel I'm ready for a new challenge." said Silvestre
"I'm really excited about this next stage of my career, hopefully playing my part in helping the club to new challenge." added Mikael Silvestre
He has become the first player to be sold to the Gunners by United since Brian Kidd in 1974.
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