Timothy who represents the United States of America at worldwide level said he was looking forward to his first training session with the team.
"I haven't played as many games as I'd like to", admitted the £15million man.
"He's looking to play me as a nine and I can't wait".
"We suffered a little bit when Moussa left in the summer, but I'm happy with these three".
The 21-year-old, who has two caps for the Ivory Coast, has scored 22 goals in 32 games this season after moving to Slovakia in March after spending two years playing in Tunisia with Étoile du Sahel.
"I went there knowing I had to put the work in to get where I wanted to be", Weah told BBC Scotland.
West Brom forward Burke and Paris St Germain youngster Weah - son of former World Player of the Year George - will see out the season in Glasgow after sealing their own switches.
"I'm like, 'Yeah, I had a meeting with the gaffer and I'm really loving the team and really loving the club and I'm going to come here'".
"It is really hard to impose yourself with such great players in front of you".
"My father has played at Celtic before".
The 18-year-old forward, already capped by United States, can not wait to get started, with his potential debut coming at home to Airdrieonians in the Scottish Cup on January 19.
I didn't go to him [Neymar] and speak to him one-on-one about coming to Celtic but I kinda spoke to other team-mates like Thomas Meunier and Dani Alves.
"Sometimes people don't understand, sometimes people take the simple things in life for granted", Bitton told Celtic's official website.
"He and rest of the coaching staff are going to build me and form me into a really good player, and my teammates are going to help me mature".