When asked what the 26-year-old will bring to the club, Klopp told Sky Sports: "Quality. That's why we got him, that's why we were interested in him. It's quite difficult at the moment because technically he's still a Southampton player.
"We don't make the prices, the market does. Liverpool supporters should forget about the price.
"We only talk about the player and what he can bring in; the quality, the mentality, the character. That is why we are really happy about it."
"Virgil hasn't had the best first half to the season at Southampton," added Klopp.
"He was out injured for a long time and we all know about the things that happened last summer.
"He's a tall player - they always need a little bit longer especially after being out for around nine months - but that's no problem. We already have quality here in that position so we don't have to rush anything.
"He needs to adapt to our style of play. It's a completely different game, but we are 100 per cent sure he will do it."