The 18-year-old joined City from Shamrock Rovers in February 2019, having made his first-team debut at 16.
He was initially brought through the youth ranks at City, but was recently included in Pep Guardiola's Champions League squad for the Lyon tie.
"This is the opportunity that I have been looking for," Bazunu said.
"I really enjoyed the first- team football that I got at Shamrock Rovers and I just can't wait to get back into it again.
"That's where you gain experience and, how, I believe, you improve at the fastest rate, so I just can't wait to get started."