Jannik Vestergaard has joined Southampton on a four-year deal from Borussia Monchengladbach.
The defender will cost Southampton £18m, according to Sky sources, after he completed a medical on Thursday.
West Ham were interested in Vestergaard, who was part of Denmark's squad for the World Cup.
"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," said Vestergaard.
"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."
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Southampton manager Mark Hughes said the club had to "fight off a lot of competition" to bring in the 6ft 6in defender.
"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," said Hughes.
He added: "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."
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