The 18-year-old - who is son of former Ballon d’Or winner and current Liberian president George Weah - joined up with Brendan Rodgers’ squad in Dubai after completing his move.
He was won over on the move to the Ladbrokes Premiership after meeting his new head coach at Celtic Park.
Weah believes his career will be in good hands as he looks ahead to the next six months under Rodgers.
The eight-cap United States international said: “We had a meeting when I came to visit the stadium and the training ground.
“The coach told me he just wants to see me playing my game, helping the team by making runs into spaces and stretching the game.
“He’s looking to play me as a nine and I can’t wait. I’m so excited to be here. I feel like the coach has a great plan for me and I think he’ll help me develop as a man.
“The little bit of experience I have will benefit me but I feel that by being here, learning from all the other guys and the coaching staff, combined with hard work and dedication, then I’ll be able to give the fans what they want.
“It’s a great honour joining this historic club.
“I’m so happy to have joined Celtic and to be with this great team and amazing coaching staff. I can’t wait to play my first game in front of these amazing Celtic fans.
“To be blessed to do that at such a young age is an amazing opportunity.”
Weah has already caught up with one familiar face in the Celtic squad after being reunited with former PSG academy classmate Odsonne Edouard.
The Frenchman performed so well on loan from the big-spending Ligue 1 outfit last season he convinced Rodgers to splash out £9million to make his stay in Glasgow permanent.
Now Celtic’s latest Parisian import hopes to make a similar impact.
Weah said: “It’s funny as the day I had the visit, Odsonne messaged me on Instagram and said, ‘Hey bro, are you coming?’
“I was like, ‘Yeah, I had a meeting with the gaffer and I’m really loving the team, I’m really loving the club so I’m going to come’.
“He saw me today in the locker room and he was laughing and joking. We were catching up. It’s great to see him again and how he has progressed and his development at this club.
“Hopefully I can do the same here at Celtic.”