The Holland U21 international, who arrived in Glasgow on Thursday for a medical, has agreed a four-year contract with the Hoops.
Van Dijk is Celtic's second signing this month, with striker Amido Balde also arriving from Portuguese club Vitoria Guimaraes.
A statement from Celtic read: "Celtic are delighted to announce that defender Virgil van Dijk has joined the club from FC Groningen.
"The Dutch Under-21 international has signed a four-year deal with the Scottish Champions, and he becomes the latest player to join Neil Lennon's squad during the close season following the arrival of striker Amido Balde from Portuguese side, Vitoria Guimaraes."
The highly-rated 21-year-old is confident he has the attributes to succeed both with Celtic and in the Dutch national set-up.
"Celtic is the biggest club in Scotland and they also play in the Champions League. They're a fantastic club and when Celtic came in for me I was so excited," van Dijk said.
"Everything here is good so I can't wait to get started. I hope to play many games for my country in the future but first of all I want to make things happen here.
"I'm a strong defender and I'm good in the air, but I also like to play football on the ground, and I hope that we'll do even better than we did last season."