The France international ended his seven-year stay at St Mary’s earlier this week by making a £25million move to free-spending Manchester United.
Saints have quickly reinvested that money by bringing in Feyenoord captain Clasie on a five-year deal, with the fee understood to be worth up to 12million euros (£8.4million).
“It feels good to be joining Southampton,” Clasie said. “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 (Koeman) 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 the games. I hope that I have many good moments and good years here.”
Clasie knows Southampton manager Koeman well from his time coaching Feyenoord, where the midfielder made 129 appearances after coming through the youth set-up.
The midfielder has 11 international caps and one of his first matches for his new club could be against his former team in next Thursday’s friendly in Rotterdam.
Southampton’s executive director of football Les Reed said: “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 Cedric 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.”