The 21-year-old centre-back signed a four-year contract on Friday after the Hoops finalised his transfer from FC Groningen for a fee that could be worth a reported £2.5million.
Van Dijk, who follows 22-year-old Portuguese forward Amido Balde in joining Celtic this summer, watched his new team-mates beating Barcelona on television last season on their way to the last 16 of Europe's premier competition and cannot wait to start this season's campaign.
He said: "Celtic is a big club, the biggest in Scotland of course.
"Celtic are also famous in Europe. I watch the Champions League all the time and you see Celtic all the time. Last year's game against Barcelona was a famous game."
Van Dijk could soon get the chance to play in Europe as Celtic begin their Champions League qualifying campaign in mid-July with their first opponents to be decided in Monday's draw.
And the defender has his sights firmly set on the making the group stages.
"I'm very confident but first of all I need to get used to the Scottish people and everything," he said. "Everything is new for me. I have left my whole life in Holland so this is a big step for me.
"I have seen a couple of players yesterday and they welcomed me very warmly. It's a warm club. The people welcomed me very warmly. The fans are also amazing, everyone knows that."
- Sports & Recreation