Van Dijk joined the Saints from Scottish Premiership champions Celtic on a five-year contract in the summer transfer window.
Southampton boss Koeman has revealed that he wanted to recruit the 24-year-old from Celtic last year.
Southampton FC (@SouthamptonFC) September 10, 2015
Van Dijk was one of the best players for Celtic for the past two years and was arguably the best centre-back in the Scottish Premiership.
It will be interesting to see how the Dutchman does in the Premier League, especially as there will be pressure on him to hit the ground running at Southampton.
The Saints will return to league action on Saturday afternoon, when they take on West Bromwich Albion away from home at The Hawthorns.