Cleverly successfully defended his WBO world light-heavyweight title in a bout against Bellew back in 2011, but the fighters will meet again in a couple of months at cruiserweight.
"I cannot wait for this," said Cleverly. "I beat him in front of his people before and this time I'm going to knock him out in front of his people. There will be no final bell in this fight, it's going to be brutal.
"Expect fireworks from the build-up, the press conferences, the weigh-in and the fight but also expect the same result. A Nathan Cleverly victory and then I will become a two-weight World champion."
Bellew added: "I want this more than any fight in the world. I've dreamt about this moment, about putting this right, about ending him. His face will be in my mind every day in camp, every night.
"I can't explain how badly I want to knock him out and that's exactly how it will end in November. For the people of Liverpool, expect a great occasion, an epic build up and an emotional fight."
The November date will be confirmed in a press conference in Liverpool next Wednesday.