The 21-year-old admitted earlier this week he was interested in a move to Scotland with his club FC Groningen revealing they would be selling him this summer.
Van Dijk is under contract with his club for another two seasons but, after turning down an approach from Brighton last summer, they are not going to stop him trying to further his career abroad.
The Eredivisie side are believed to be looking for a fee in the region of £2.5m for the player, who has represented his country at U19 and U21 levels.
"I'm happy to be here. Celtic is a big club," he said on arriving in Scotland. "It's very close [to being completed]. I think I only have to do the medical but we'll see what happens.
"The promise of more nights like Celtic's Champions League win against Barcelona was part of the attraction of moving to Scotland.
"The game against Barcelona was a big game and I watched it at home. It was a very good game and I look forward to playing in the Champions League as well.
"It's difficult to say but I'm a defender who likes to play football. I'm not a defender who plays the long ball all the time.
"There were a lot of clubs interested but nobody was as concrete as Celtic. I'm happy to be here and I would love to play for Celtic."