The 17-year-old defender signed a a long-term contract with the Premier League club.
Van den Berg played 15 matches in the Dutch top flight last season, helping Zwolle finish 13th.
Speaking about the move, Van den Berg said:
It’s just an amazing feeling.
It is, for me, the biggest club in the world and it’s a dream come true. I am really excited.
I’ve seen what kind of players from the Academy grew into the first team here. It is unbelievable, especially when this kind of big club does that.
Of course, the trainer [Jürgen Klopp] is a great guy and one of the reasons they are successful – and also one of the reasons I came here.
I think this is the best place for me to grow and hopefully play a lot of games here.