Rodgers, who has also signed West Bromwich Albion (WBA) winger Oliver Burke on loan for the rest of the season, is delighted to have snapped up Weah and believes he has plenty to offer.
Weah - son of former Ballon d'Or victor George, now president of Liberia - will spend the rest of the 2018-19 campaign with Brendan Rodgers' Scottish Premiership leaders.
The new arrivals are a welcome boost for Rodgers after a frustrating first half of the season which saw main goal threat Odsonne Edouard struggle with injury and consistency, while Leigh Griffiths is taking time away from the game to concentrate on personal issues.
But, with three new options now available to him, the Northern Irishman is confident his side have all the firepower they need as they look ahead to the second part of the campaign. "He has told me it is really intense and it is good to grow as a footballer by playing for this club".
"I haven't played as many games as I'd like to", admitted the £15million man. The style will always be the same, but it increases the way we can play.More news: Bayern Munich to sign Benjamin Pavard from Stuttgart at end of season
More news: Harden's fifth straight 40-point game helps Rockets top Warriors in OT
More news: Kendall Jenner's 'Most Raw Story' to Help People Disappoints Everyone
"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".
Bayo, who has cost the Scottish champions a fee in the region of £2 million, will join from Slovakian club Dunajska Streda, where he has scored 18 goals in 23 matches this season.
Weah is only here for six months, but we have a feeling, should things go well, Celtic could snag the striker for a full season next term.
Timothy Weah was unveiled as a Celtic player on Tuesday.
But Parkhead sources have denied the reports, just days after Celtic insiders confirmed another MLS player, Houston Dynamo forward Alberth Elis, was not on the club's radar.