The 23-year old centre-half has signed a three-year deal with the Bhoys, joining from Israeli outfit Ashdod, and is eager to start working with his new club.
"It has been a long day, but it has been worth it. 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.
"I would like to thank God for everything and to thank the manager and directors here at Celtic - who have placed their trust and confidence in me."