The 19-year-old, who can also play in midfield left Fulham this summer after joining from Castlebar Celtic in 2013.
Despite injuries disrupting his first season at the Club, Baba became a regular in Fulham’s U18 and U21 sides.
Born in Cameroon, he moved to Ireland with his family at an early age and became the first African-born player to captain a Republic of Ireland age group when he led the U17s.
He has since gone on to represent his country at U19 and U20 level.
Baba told bcfc.com that he's looking to kicking on his career with Blues.
"I've been training here for the last month and it's been very good," he said.
"I'm very pleased and I think it's a very good opportunity for me.
"I just want to kick on and start again with something I love doing."