The transfer fee of £70 million ($94 million) could reach £75 million ($100 million) depending on Van Dijk's achievements at Anfield.
He finally became the world's most expensive defender on Wednesday, with Liverpool having pulled out of a £50million move in the summer after Southampton complained to the Premier League about an alleged illegal approach from the Reds.
The now Leicester boss had Van Dijk as his skipper at Southampton last season as the Saints fought to keep the centre-back.
While most of the arguments around the transfer were based on the huge fee, valid points were raised on the question marks over van Dijk's attitude and the fact that it can be perceived to be something of a desperation move from Jurgen Klopp to turn out his pockets in order to try to solve his defensive woes.
Asked what the 26-year-old will add to Liverpool, Klopp told Sky Sports: "Quality". It's quite hard at the moment because technically he's still a Southampton player. We do not make the price, the market makes the price and the first thing all Liverpool supporters should forget quite soon is the price. We only talk about the player and what he can bring in - his qualities, mentality and character.
GETTY Virgil van Dijk was in attendance for Liverpool's clash with Leicester
"I am happy for him and happy he can't play against us".
The Netherlands worldwide completed a £75million move to Liverpool from Southampton on Wednesday and became the most expensive defender of all time in the process. "That is why we are really happy about it".
"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".