The 25-year-old -- who was in the Denmark World Cup squad but didn't figure in any of their four matches -- signed a four year deal for an undisclosed fee from German side Borussia Moenchengladbach.
Vestergaard is the fourth signing by Saints boss Mark Hughes in the close season and will it is hoped become as assured a figure as van Dijk was before he secured a record transfer for a defender -- £75 million (84.6m euros, $98m) -- to Liverpool last January.
"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," he said on Southampton's website.
"I feel I'm at a really good place to develop."
Vestergaard, who has spent his professional career in Germany joining Hoffenheim aged 17, admitted the extra press attention will take getting used to.
"Every Danish guy loves to see himself in the Premier League -- it is the biggest league in the world and a very attractive place to play," he said.
"I think there is more awareness in the Premier League that will take some getting used to -- the press side of things -- but experience is always positive, and having about 200 games in the Bundesliga will make it easier for me to adapt.
"I'm quite a big guy and a physical guy, so I'm going to try to help the team in that way."
Hughes, who signed a permanent contract after saving the club from relegation, said Vestergaard's signing was especially pleasing as other clubs had been interested in him.
"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," said Hughes.
Aside from Vestergaard the 54-year-old Welsh manager has also brought in highly-rated goalkeeper Angus Gunn from Manchester City, Norway forward Mohamed Elyounoussi arrived on a five-year contract from Swiss outfit Basel and Scotland international Stuart Armstrong joined from Scottish champions Celtic.