Despite not getting on the pitch, Vestergaard was part of the Denmark squad that competed at the World Cup in Russia this summer, and he has 16 senior caps to his name.
The 6ft 6in centre back becomes the club's fourth signing of the summer, following the arrivals of Stuart Armstrong, Mohamed Elyounoussi and Angus Gunn.
Speaking about his latest signing, Mark Hughes told southamptonfc.com: “We have had to fight off a lot of competition to bring Jannik here, and we are delighted he has chosen Southampton as the right place to take the next step in his career.
“Although we were aware of the level of interest in Jannik, he made it clear very quickly that the quality of the club and the ambitions we have here meant this was his number-one option.
“He represents another excellent addition to our squad this summer, and brings with him an extensive amount of experience for his age. That means he can not only help us in the present, but that he has the potential to develop his game even more with us, which is what we want as a club and is clearly exciting for both parties.
“One of our intentions this summer was to strengthen our aerial presence, and Jannik can help us do that not only defensively, but also in the opposition penalty area.
“His character and the leadership qualities he has shown in an intense division like the Bundesliga have been impressive, and, as a club, we have been following him for some time now, so we are naturally delighted to have been able to bring him to Southampton.”
Vestergaard himself revealed he is 'very excited' to make the move to the south coast, and was drawn to the club by their strong desire to sign him, as well as his own research that he conducted once he heard of the club's interest.
“It feels great. The deal has been under way a couple of days and I’m very excited now it has finally happened.
“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.
“The degree to which the club wanted me was important in my decision. They had done a lot of research, seen a lot of live games and on video as well. I feel I’m at a really good place to develop.
“After seeing the place, I have only seen nice people and smiles on faces. I feel very welcome.”