Banks was Steward's assistant, and has been in charge of the Ukrainian's training since September.
Klitschko told Sky Sports News: "I knew from the beginning it was going to be Johnathon Banks.
"He is a man who has learned a lot from Emanuel and whom I met on the same day as I first met Emanuel nine years ago.
"Of course he is not Emanuel Steward but he is Johnathon Banks, and everyone has their own way of doing things. Considering everything, this camp has gone very well."
Banks, 30, is still an active fighter, having won 30 of his 32 professional bouts.