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.
Gunners boss Arsene 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."
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."