The 23-year old Scotland striker has been linked with the Scottish champions for the past few weeks and has now finalised his transfer to Celtic Park.
Griffiths told Celtic's official 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.
"Unfortunately, it's taken to the last day but I'm just glad that it's been done now and I can't wait to get started.
"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."
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