Koeman signed Van Dijk from Celtic for a fee that the Glasgow Evening Times valued at £13 million over the summer transfer window, and the centre-back has gone on to impress in his initial appearances, scoring his first goal for the club in their 3-1 victory against Swansea City at the weekend.
The powerful centre-back headed in from a corner in the match, and Keoman believes his new centre-back will only get better as he becomes accustomed to life in the Premier League.
"One of his qualities is he is a good header of the ball," he said. "He is also defensively strong and his personality is important for the team.
"He's only 24, it's his first season in the Premier League and he will get better."
Koeman has shown faith in Van Dijk since he arrived at Southampton, and thrown him straight into his defence alongside Jose Fonte.
The Dutch international has repaid his trust with his performance levels, and he is very much enjoying his time in England.
"I'm very pleased," Van Dijk said. "It's been a dream come true already by playing in the Premier League.
"But scoring my first goal feels amazing and to get the three points as well makes it even better."
Van Dijk's good form will not come as too much of a surprise to anyone who saw him play at Celtic, where he became a key player.
The 24-year-old is assured in possession and reliable defensively, and he looks to have been another excellent addition from Southampton, who have made a habit out of bringing in top quality over recent transfer windows.