Van Dijk joined Southampton from Scottish Premiership champions Celtic on a five-year contract in the summer transfer window.
The 24-year-old centre-back made his debut for the Saints against West Brom at The Hawthorns and gave a good account of himself.
Van Dijk, who played for the entire 90 minutes, had a pass accuracy of 86% and won all three of his headers against the Baggies.
Koeman was delighted with the performance of the former Groningen star and told The Daily Echo: “Virgil was in my opinion impressive how he played today.
“Looks very comfortable with his new teammates and good in defending and we know also one of his qualities is in his passing from the back. He played perfect today.”
Van Dijk was one of the best players for Celtic for the past two years and was the best centre-back in the Scottish Premiership.
There was pressure on the Dutchman to hit the ground running at Southampton, and it seems that he has responded positively to that.