The 21-year-old Ivory Coast forward joined Dunajská Streda in March last year, having previously spent two years playing in Tunisia.
Ahead of his move on loan to Celtic, the PSG hierarchy were quick to tie up the American to a new deal signalling how much the club rate the youngster - especially with the lack of an "option to buy" clause as part of his loan switch to the Scottish champions.
"He's been in the PSG squad and featured for them in pre-season".
"It's a fantastic honour to sign for such a historic club, and I'm really looking forward to this opportunity. That'll be interesting. I've never been before so I'm really excited for that".
Weah said he "received "a lot of offers" to go on loan this winter, but Celtic was the one that stood out for him".
"He and rest of the coaching staff are going to build me and form me into a really good player, and my team-mates are going to help me mature".
PSG allowed the 18-year-old Weah to leave on the day he signed a contract extension with the French team until June 2021.
He becomes Brendan Rodgers' third signing of the January transfer window following the loan arrivals of Oliver Burke and Timothy Weah.
Italian Serie A side Parma lost out to Celtic in the chase for striker Vakoun Issouf Bayo.
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