Brown was the Dutchman's captain during Van Dijk's two years north of the border.
He said: “Virgil van Dijk is a Rolls-Royce. He cruised it in the SPL and he's cruising it in the Premier League – he has now shown that he is the best defender in the world.
“Virgil has that willingness to win, a willingness to get better – he improves week in, week out.
“He makes good players believe they can be great players as well, and what he has done at Liverpool too is steady the ship.
“He has made that team a hard team to beat and that is due to his work-rate. It's the drive in him, more than anything – you look at him and feel confident.
“One person in the Premier League has beaten him in a one-on-one in 75-odd games. So it's that confidence and belief that he puts in you that oozes through the team."