Clasie, who has cost the Saints a fee of around £8.4m, is seen as a direct replacement for Morgan Schneiderlin, who left for Manchester United earlier this week.
The 24-year-old has 11 international caps and was part of Louis van Gaal’s squad for the 2014 World Cup finals.
Clasie has been with Feyenoord for most of his professional career – spending one season on loan with another Rotterdam side Excelsior – and made his debut in Ronald Koeman’s first game in charge.
“It feels good to be joining Southampton. It’s a nice club, and I’m happy to be here,” Clasie said. “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.”