Ambrose flew in to Glasgow on Friday morning and, following a medical at Ross Hall, has joined the Bhoys on a three-year deal.
The 23-year-old, who can play at centre-back or in midfield, will boost Neil Lennon's options after they sealed a place in the Champions League group stages following a 4-0 aggregate win over Helsingborgs on Wednesday night.
"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 the club'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.
"I am the kind of player who plays where it is of benefit to the team. If the manager trusts me to play in midfield or defence, then I trust him and I am the kind of player who will give 100 per cent, whatever the coach asks of me."
Ambrose enjoyed three years with FC Ashdod, and thanked his former side for giving him the chance to progress as a player.
He added: "The move to Israel really opened the door for me and gave me my opportunity. I had been to other clubs, but they were the ones who gave me my chance.
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"For that I would like to thank the coaches and directors at FC Ashdod, my agent Dudu Dahan and also my colleagues and the fans – who all helped develop me as a player."
Following Celtic's impressive qualification for Europe's top club competition, Ambrose is looking forward to the challenge of a tough group
"I have come here to find we are in the same group as Barcelona, Benfica and Spartak Moscow," he continued.
"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."