Ambrose has signed a three-year contract with the Scottish side.
"Today is one of the happiest days of my life, signing for one of the biggest clubs in the world - a club I have known about since I was young," Ambrose told Celtic's official website.
"I just can't wait to get started, to play in front of the fans and call this place home."
Ambrose is looking to feature for Celtic in the Champions League.
"I have come here to find we are in the same group as Barcelona, Benfica and Spartak Moscow," Ambrose added.
"It's a lovely group, you might call it the group of death and it will be hard, but hard work always pays.
"I am just looking forward to meeting my team-mates now, there is no better place for me than Scotland."