The 21-year-old moved to Groningen from Willem two years ago, and admitted that he was looking forward to playing in the Champions League.
Groningen confirmed last week that a bid had been made for the defender.
"Celtic is a big club and it is fantastic to be here," said Van Dijk, arriving at Glasgow Airport for talks, according to BBC Sport. "They play in the Champions League and that is a big thing for me.
"I am a defender who likes to play football, not a defender who plays the long ball all the time.
"The [Celtic] game against Barcelona was a big game and I watched it at home. It was a very good game. I look forward to playing in the Champions League."