The striker told his new club's website: "I'm over the moon. It's been a long time coming. Ever since I heard Celtic were interested there was only one place I wanted to play and I'm just glad it's done now.
"It was the middle of December and my agent gave me a phone and said Celtic could be interested in January and I have just been counting down the days.
"We are the Scottish champions to begin with, and this is a massive club with a massive fanbase and a massive stadium. I have watched the Champions League nights on the TV and there is no better place to play. This is where I want to be."
Griffiths has scored 12 goals for Wolves in League One this season.