Fox completed the move to Parkhead with the fee officially being undisclosed or between £1.5m (according to Sky Sports) and £3m depending on what you want to believe.
The defender/midfielder signed a four year deal and told Celtic's official website: "I'm a bit shellshocked, but I'm really grateful to the manager and the coaching staff for bringing me here. "It's a dream come true.
"It's all happened so fast but I'm delighted to be here. I got a phone call on Thursday afternoon to tell me to head for Glasgow and it's all been a bit surreal.
"This is a massive move for me. I couldn't sleep on Thursday night because I was so eager to get down and meet the lads in London and I can't wait to make my debut.
"The size of Celtic speaks for itself. You have the history, the fanbase, the stadium and there's the added bonus of European football.
"I want to test myself at the highest level and there is no better place to do it than at Celtic. I'm just looking forward to getting started."