Burke has joined Celtic on a six month loan deal from parent club West Bromwich Albion - for whom he has only made three league appearances this season.
The Scottish champions had a bid for Bayo rejected last week but have now completed the signing of the 21-year-old, who has been capped twice by the Ivory Coast.
Timothy Weah, the 18-year-old US forward with Paris Saint-Germain (PSG), has joined Scottish champions Celtic on a six-month loan deal, the Glasgow club announced on Monday. "He's the right man to help me develop and get the best out of me".More news: Students and fans of Clemson University celebrate championship
"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'".
Those two deals even provoked Celtic legend Chris Sutton to claim that Rangers are now favourites to win the Scottish Premiership title.
"I am in love with Celtic so I am really happy", he told BBC Sport.More news: Susan Boyle triumphantly returns on 'AGT: The Champions'
'Can't wait to get started and get the chance to play in front of those fantastic fans I've heard so much about. I'm so excited to be here. He'll join Celtic during its winter training camp in Dubai, where he'll look to make an instant impact on manager Brendan Rodgers.
"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 great to see him again and it's great seeing how he has progressed and seeing his development at the club and, hopefully, I can do the same". Physically he's very good, very fast and is a strong player.More news: Mohamed Salah voted African Footballer of the Year