The midfielder has agreed a five-year contract and joins from Dutch side Feyenoord, where he has been captain in recent years.
24-year-old Clasie has 11 caps for his country, featuring for the Oranje as they finished third at the 2014 FIFA World Cup finals.
Other than a season-long loan spell at Excelsior, Haarlem-born Clasie has spent his entire professional career with Feyenoord. He made his debut aged 20, in Ronald Koeman’s first game in charge of the Rotterdam club.
Executive Director of Football Les Reed commented: “Jordy is one of the most highly sought-after midfielders in Europe.
“His qualities are plain to see for anybody who has watched his development over the past few years as closely as we have, and we are delighted that he will continue his growth at Southampton.
“Like Cédric Soares and Juanmi, he has emerged from an academy with a set of values closely aligned to our own and has spent the entirety of his prior professional career contracted to one club.
“With Jordy having played for Ronald Koeman for three years at Feyenoord, this is the perfect move for both the player and Southampton Football Club.”
Clasie added: “It feels good to be joining Southampton. It’s a nice club, and I’m happy to be here.
“It’s a big club playing in what I think is the biggest and most important league.
“Ronald being here is a big thing for me and that was important in me coming here, but even if he wasn’t here, I’d have come to this club.
“I played every game for him. He’s a good trainer and a good man so I like him, but I came here not only for him. I came here for the club.
“I’ve watched many games of Southampton, and it’s felt good when I’ve watched these games.
“I hope that I have many good moments and good years here.”