The 26-year-old midfielder moved to Birmingham in June following a five-year spell with the Dons.
Despite having to end his association with the League One side, Gleeson admits that making the step up to the Championship was an easy decision.
"I felt around January that I knew it was time to move on. When Birmingham came in for me it was a no-brainer," the Irishman told the Birmingham Mail.
"I was not too worried about the football side of it. I've always felt I would be okay in the Championship, compete and not look out of place.
"The main thing I found when I came was the fitness levels. The lads are tremendously fit, but fitness-wise and football-wise, I've got confidence in myself and this was a move that I had to make."
Gleeson has made six appearances for Birmingham in all competitions this season.