The defender has signed a four-year deal at the club for a £18 million fee, as reported by 'Sky Sports'.
Vestergaard was part of Denmark's World Cup aquad in Russia over the summer, and has won 16 caps for his national team since making his debut for them in 2013.
The 6ft 6in centre-half has spent the majority of his career in the Bundesliga were he played for sides such as Hoffenhiem, Werder Bremen and most recently Borrussia Monchengladbach.
He made 84 appearances for his latest club over two seasons, in which he gained experience in the Champions League and the Europa League.
“It feels great. The deal has been under way a couple of days and I’m very excited now it has finally happened." Vestergaard told Southampton's website.
“I knew of the interest before the World Cup and the club has followed me for quite some time and done a lot of scouting, which is also a good sign for me that they know my strengths and weaknesses."
Manager Mark Hughes was happy to get the signing over the line after they faced competition from other clubs for the Dane's signature. This is his fourth addition to the squad this summer, alongside Stuart Armstrong, Stuart Armstrong and Angus Gunn.