Koeman 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 a fitness coach.
The former Holland international replaces Mauricio Pochettino, who left for Tottenham last month.
Southampton executive director Les Reed said in a statement: "From the moment we met with Ronald, it was clear he had the vision and ambition to take our club forward, that he shared our football philosophy and could see the opportunity to move our club to the next level.
"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.
"Ronald's passion for the opportunity here at St Mary's was very clear, and we look forward to continuing our growth with him as part of our team."
Koeman arrives following a three-year spell at Feyenoord, who he led to consecutive top-three finishes in the Eredivisie.
He has also won the Dutch title with both Ajax and PSV Eindhoven, the Copa del Rey at Valencia and coached Vitesse, Benfica and AZ Alkmaar during a 14-year managerial career.
Koeman comes with a reputation for an attacking brand of football and a commitment to promoting young talent which will sit well with Southampton who have nurtured the likes of Gareth Bale, Alex Oxlade-Chamberlain, Adam Lallana, Luke Shaw and Calum Chambers in recent seasons.
Koeman said: "I am thrilled to be the manager of Southampton Football Club.
"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 a talented first-team squad, a world-class academy and the infrastructure to sustain success in the Premier League.
"The opportunity to continue the development of this famous football club was simply too good to turn down
I cannot wait to get started."
Source : PA