Koeman replaces Mauricio Pochettino, who left for Tottenham Hotspur after guiding Southampton to eighth in the Barclays Premier League last season.
The former Dutch internationalist is joined at St Mary's by his older brother Erwin, who has been named assistant first team manager, and Jan Kluitenberg, who will be an assistant and fitness coach.
Koeman said in a statement: "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 a talented first-team squad, a world-class academy and the infrastructure to sustain success in the Premier League. I cannot wait to get started."