The 21-year-old signed a five-year contract after Dinamo Zagreb accepted Celtic's offer and he is set to go straight into the side to replace Virgil van Dijk after the Dutchman's move to Southampton.
Simunovic told Celtic's website: "I am absolutely delighted to join Celtic. I know what a huge club I am joining, one of the biggest in Europe, and I know about its history and its great supporters.
"I can't wait to get started and join up with my new team and begin my career at Celtic.
"I am looking forward to this move very much, I am desperate to get to Scotland and play at the famous Celtic Park."
Celtic pushed through his signing late on deadline day after agreeing a fee with the Croatian champion that includes a significant sell-on percentage.
Simunovic, who played against Celtic in the Europa League last season, said: "I know we have a lot to play for this season and there are many exciting times ahead, this is my reason for joining Celtic.
"I want to win things in my career and I think I can do this at Celtic. All I can promise the supporters is that I will be giving everything I have in every game to win and bring some good moments to our fans."
