"It's just an amazing feeling. It is, for me, the biggest club in the world and it's a dream come true. I'm really excited," Van den Berg told the club's website.
"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."
Van den Berg made 15 appearances for Zwolle last season, as they finished 13th in the league.
The Netherlands under-19 international said he was keen to further his development under Liverpool boss Juergen Klopp.
"Of course, the trainer is a great guy and one of the reasons they are successful -- and also one of the reasons I came here," Van den Berg added.
"I think this is the best place for me to grow and hopefully play a lot of games here."
Liverpool finished second behind Manchester City in the Premier League last season before defeating Tottenham Hotspur 2-0 in the Champions League final.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Toby Davis)
