The south coast club have been searching for a new boss since Mauricio Pochettino departed for Tottenham last month.
And former Netherlands international Koeman has taken the reins at St Mary's Stadium, with brother Erwin and Jan Kluitenberg named as his assistants.
The 51-year-old expressed delight at his appointment, telling the club's official website: "I am thrilled to be the manager of Southampton Football Club.
"The opportunity to continue the development of this famous football club was simply too good to turn down.
"From my very first meeting with (head of football development) 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."
Koeman enjoyed a stellar playing career, winning the UEFA European Championships with the Netherlands in 1988, as well as the European Cup on two occasions with PSV and Barcelona.
He scored the winning goal to secure glory for Barcelona in 1992, finding the net with an extra-time free-kick to beat Sampdoria 1-0 at Wembley.
As a coach, the 51-year-old won two Eredivisie titles at Ajax, a third at PSV in 2007, and the Copa del Rey with Valencia a year later.
Koeman revealed in February he would be leaving Feyenoord at the end of the campaign after three seasons in charge. The club went on to finish second in the Dutch league, four points behind champions Ajax.
