Klopp named Van Dijk as his new captain on Monday after Jordan Henderson joined the influx of star players to the Saudi Pro League.
Trent Alexander-Arnold will serve as Van Dijk's assistant.
Van Dijk joined Liverpool from Southampton in January 2018 and has made 222 appearances in his time at the club.
The 32-year-old has won the Premier League, UEFA Champions League, FA Cup, League Cup, UEFA Super Cup and FIFA Club World Cup in his time at Liverpool.
Elaborating on his decision to appoint Van Dijk as his new leader, Klopp told Liverpool's website: “My reaction? It was my decision. We had to make the decision and I had to think about it. But with Virg it's really now not difficult because I think he's an absolutely natural follower of a really big personality with Hendo, and we had to replace James Milner as well. Is that possible with one person? Probably not, so that's why it's really important that we speak, maybe a little bit later, about the leadership group, which is a really important group of people. But Virg has everything to wish for to be a captain of a football club. Number one, he's probably, let me have a think, definitely the best-looking captain in the Premier League, which is important for team pictures! But, of course, personality-wise everything is there.
“He wants to be a leader, he is a leader. He has to step up, like all of us have to step up because we were used to things how they always were and now we have to create something new – a new structure, a new culture – and that's really exciting. He will play a massive role in that – he has to. With the captaincy now, I'm pretty sure in the moment he feels the pride, he feels the honour. The busy stuff of it, the work behind it, he will feel from now on and that's good. We will do that all together, we all will help him. But I think it was the absolute logical decision. When I saw his reaction, I was really happy for him because I was captain of Mainz 05 for a while, which is a nice thing to have but I never felt these kind of things. But obviously being captain of Liverpool FC is completely different. I saw he was really happy about it, so I was happy about it and now we can start working.”