Klitschko, who is preparing to defend his WBA, IBF and WBO belts against unbeaten Pole Mariusz Wach in Hamburg on Saturday, had been training with Steward's former assistant Banks since Steward was taken ill in September.
There had been much speculation over Klitschko's move to replace Steward given that Banks, 30, is six years Klitschko's junior and is still an active heavyweight fighter himself.
Klitschko said: "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.
"We are all missing Emanuel, who was a great friend and one of the geniuses of the sport. But his spirit is with us and I know he is around us and looking forward to this fight."
Banks, who has won 30 of his 32 professional contests and is due to fight in Atlantic City on November 17 against Seth Mitchell, said he is keen to make the most of a unique situation.
Banks said: "It's an amazing situation on both sides but I don't feel any extra pressure. It's not like I'm training a guy for a golf tournament. I'm with a fighter who has a fight, and I have a fight coming up too."