The 26-year-old centre-half, a non-playing member of Sweden's World Cup squad, will move to St Mary's for £2m on a four-year deal.
Saints manager Gordon Strachan said Svensson would bolster what is already a strong squad.
"I am looking forward to working with Michael next season," said Strachan.
"He will broaden my defensive options and strengthen a squad which already has some first-class professionals."
Southampton chairman Rupert Lowe added: "I met with Michael yesterday and was very impressed with his professional attitude.
"I look forward to working with him and all our staff to build on the success of last season."
Svensson, who has won 12 caps for his country, played in his homeland for Skillingaryds, IFK Vernamo and Halmstads - where he earned two Swedish league winners' medals.
He moved to Troyes last season, making 23 appearances, and will now join his international team-mate and namesake Anders Svensson at St Mary's.
"I am really excited. It has always been my dream to play in the Premiership and I know from talking to Anders that Southampton is a really good club," Svensson told the Saints' website.
"There are good coaches and players here and he told me it is a nice city and a friendly place.
"I have only been here a day, but my first impression confirms that.
"The stadium is fabulous and it has obviously given the club a big boost in the right direction.
"They have a stable team in the Premier League and it is one which could climb higher and progress.
"I hope I can be part of that and I cannot wait to get going."