Griffiths has impressed in League One this season, scoring 12 goals, and also thrived during a loan spell in Scotland last season with Hibernian.
The 23-year-old becomes the second striker to leave Molineux on transfer deadline day after Kevin Doyle joined Queens Park Rangers.
Celtic are 18 points clear at the top of the Scottish Premiership and Griffiths said: "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.
"I want to bring goals – that´s what I am all about and what I love doing. I did it last season for Hibs and have done it for Wolves and now it's my time to shine in the Hoops and hopefully I can do it."
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
