"It's great to have the opportunity to put things right," BBC Sport quotes Bellew as saying.
"I have to get my head down and work doubly hard in the weeks ahead of the fight to make sure the job gets done properly this time around."
Bellew and Chilemba met at Liverpool's Echo Arena last month, with the fight ending in a stalemate.
The Bomber, who was criticised for his performance during the match, insists that he has learned from the experience.
"I've had a bit of stick but I can take it and I've learned from what happened," he added.
"It'll be a different fight this time around. The first fight should've been a great one but it just didn't work out that way.
"I won't be making predictions this time, just concentrating on working hard and beating Isaac to land that world title shot."
Bellew vs. Chilemba will take place at the O2 Arena on May 25.