The Reds have splashed out a world record-breaking deal for a defender after going close to securing his signature in the summer.
The 26-year-old will not be able to play against Burnley on New Year’s Day but could make his debut in the FA Cup third-round clash with Everton.
His record-breaking move to Liverpool was finished on Wednesday, with the deal was finalized on the first day of the transfer window on Monday, and he told the club site: ‘I am glad to be here and I can hardly wait to begin.
‘I think the most essential thing is the extent of the club, the way of life of the club, the players, the manager and clearly the fans, who make the club this extraordinary.
‘With the history at the club and everything around it – even the preparation ground and stuff – it is only a flawless, consummate match for me, and an ideal match for my family too.’
Van Dijk was at Anfield on Saturday to watch Liverpool’s 2-1 win aganist Leicester, with Mohamed Salah scoring twice in a rebound triumph.
‘I think it’ll be something extraordinary,’ he said. ‘I think Anfield is an extremely uncommon stadium and it is my home right now also.
‘I am simply anticipating being on the pitch, particularly as a [home] player at the stadium. It will be pleasant, particularly the night games and the European evenings.
I hope to win trophies. Every player wants to win trophies and with this squad we have and the progress the club is making, I think we are very close to it.’Obviously we still need to do it and we will see what the future brings.’
Manager Jurgen Klopp said in the week: ‘He has to adapt to our style of play. It is completely different but we are 100 per cent sure he will do it. I am happy it is finally done but there is no rush.
‘I can imagine people will think, “Wow, what a number it is”, but for me the fee is not really interesting. 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 just discuss the player and what he can get, his qualities, attitude and character. That is the reason we are extremely upbeat about it.’
Klopp conceded Van Dijk’s wellness issues were a worry as he just played 16 times for Southampton in 2017, including 12 this season following Liverpool’s fizzled endeavor to sign him in August.
‘It was likely not his best half of the season at Southampton,’ Klopp said. ‘He was harmed and afterward we think about the things that happened the previous summer.