The 26-year-old swapped Southampton for Anfield at the start of the January transfer window in a £75m deal, five months after trying to force through a move between the clubs.
Van Dijk memorably marked his debut with a winning goal against Everton last week, and the Dutchman is willing to continue working hard in the hope of providing Reds supporters with many more happy memories.
"It doesn't make me nervous, it's a big compliment to myself for the hard work I've put in so far, that Liverpool are willing to pay that much money. I can't change anything about that," he told Sky Sports News.
"I think the size of the club, the fans, the players, the manager, the whole package here is amazing. You can see yourself that the atmosphere at every home game is amazing. I'm just very happy to play for the club."
Van Dijk overtook Kyle Walker as the most costly defender in world football, with Manchester City paying around £50m to sign the full-back from Tottenham Hotspur last summer.