Steward, the mainstay behind the legendary Kronk Gym in Detroit, passed away having recently undergone surgery for a stomach illness.
"Boxing has suffered a tremendous loss with the passing of Emanuel Steward," Wladimir said in a statement posted on the Klitschko brothers' official website.
"Vitali and I, along with the entire Team Klitschko, send our deepest and most heartfelt condolences to Emanuel's family and friends.
"It is not often that a person in any line of work gets a chance to work with a legend. Well, I was privileged enough to work with one for almost a decade.
"I will miss our time together. The long talks about boxing, the world, and life itself. Most of all I will miss our friendship.
"My team and I will carry on with the goals we had set while Emanuel was with us because that is exactly what Emanuel would have wanted. I know he will be with us in spirit along the way and we will accomplish these goals in his honour."
He signed off: "Rest in peace Emanuel. You will be greatly missed. Until we meet again my friend."
Oscar De La Hoya called Steward, with whom he worked in 1997, "one of the best and most and most respected trainers of this era."
De La Hoya said: "It brings me great sadness to hear of the passing of one of the best and most respected trainers of this era, Emanuel Steward.
"I learned a lot from him during our professional relationship and I will be for ever grateful for his help during that time.
"We were also friends and I know I am going to miss him as so many others will too. He was an important part of our boxing community."