The Dutchman has signed at three-year contract with the club after being widely tipped to replace the outgoing Pochettino.
"The opportunity to continue the development of this famous football club was simply too good to turn down. I cannot wait to get started."
The 51-year-old boasts an illustrious career and is highly decorated as both a player and as a manager.
A 1988 European Championship winner with Holland, Koeman acted as assistant to Gus Hiddink during the 1998 World Cup, but began his club coaching career as an assistant to Frank Rijkaard at Barcelona.
The Dutchman departed Feyenoord at the end of last season after guiding the club to an impressive second place finish in Eredivisie.
Executive director Les Reed welcomed Koeman upon his appointment, saying;
"The club, the players and the fans will all be excited to have a man of Ronald's experience at the very highest level joining our club."
The first job for the incoming Saints boss is likely to be the battle to convince the likes of Adam Lallana, Dejan Lovern and Luke Shaw to commit their immediate futures to the club, and work with him in the Premier League next season.