The 51-year-old coach has agreed a three-year deal as successor to Mauricio Pochettino, who joined Tottenham last month.
A former Netherlands international, Koeman has won the Eredivisie three times as a manager and most recently finished second in the Dutch league with Feyenoord.
“I am thrilled to be the manager of Southampton football club,” Koeman said in a statement. “The opportunity to continue the development of this famous football club was simply too good to turn down.
“From my very first meeting with Les Reed, I could see clearly that this was the right club for me.
“We share the same philosophy of football, and the same belief in how to develop the club.”
Southampton have also appointed Koeman's brother, Erwin, as assistant manager, and Jan Kluitenberg as first team coach.