Southampton did not disclose the financial terms of the deal but British media reports said the transfer fee was in the region of 11.5 million pounds ($17.63 million).
Van Dijk, who has represented Netherlands at the under-19 and under-21 level, becomes Southampton's second signing on transfer deadline day. They had earlier announced the signing of Harry Lewis from Shrewsbury Town.
The Saints, who sit in 10th place in the Premier League, have conceded five goals in their four matches.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Clare Fallon)
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