The 19-year-old striker agreed to a contract extension with the French club until 2020 before moving to Celtic on a temporary basis, with the Scottish champions also having the option to buy the player.
Edouard, who was loaned out to Toulouse last season, follows Jonny Hayes, Kundai Benyu, Olivier Ntcham and Patrick Roberts in joining Brendan Rodgers' squad during the window.
"I am absolutely delighted to be joining Celtic, one of the world's truly great football clubs, and I can't wait to wear the famous Celtic jersey," the Frenchman told Celtic's official website.
"I am really looking forward to meeting my new team-mates and we will work hard together to bring our fans as much success as possible."
Eduaord heads out of PSG on the day that the big-spending Ligue 1 outfit completed a deal for Kylian Mbappe, with the France international joining a well-stocked striking department on a loan deal which includes the option for a €180 million deal in 2018.