The Shrewsbury-born former Town goalkeeper has penned a three-year deal in Glasgow after leaving Tottenham Hotspur.
Hart said: “This is a great moment for me in my career and I am absolutely delighted to be joining a club of Celtic’s stature.
“I know just how big this club is and of the incredible support that it enjoys, and I can’t wait to play in front of the fans at Celtic Park. I’m looking forward to meeting up with my new team-mates now and getting to work with the squad and, in particular, the other goalkeepers here.”
The 34-year-old former England and Manchester City goalkeeper, played 10 times for Spurs last season but only in FA Cup and Europa League games. He has left Spurs for £1million with a year to go on his deal.