Haye pulled out of their planned December bout with a biceps injury.
But the two fighters have come to an agreement to get back in the ring next summer.
The fight has been rescheduled for 5 May.
“I’m pleased to get a new date in the diary and I look forward to giving boxing fans a great night on May 5,” said Bellew.
“To be honest I was looking forward to a great victory in December and a relaxing family break over Christmas, but my mind is still very much on this fight and I will punish him for that.
“I now have a very clear plan for 2018 and that is to knock out David Haye, and then knock out Tyson ‘Stavros Flatley’ Fury and end both their careers.
“But first thing’s first, I need to rid the sport of David Haye on May 5 and I look forward to doing this in what I believe will be an explosive fight.”
Bellew beat Haye in the 11th round back in March this year and talk of a rematch immediately followed.
Haye, 37, later revealed he had torn his achilles during the bout.
Haye had been training for the rematch – originally scheduled for December 17 at the O2 Arena – but slipped on some stairs while training, forcing him to withdraw.
”Tony has boasted that the rematch gives him the opportunity to force me into retirement,” said Haye.
“Unquestionably, I step into the ring on Saturday May 5, with both my career and legacy on the line.
“After my freak accident down a stairwell last month, I was heartbroken not to give everyone the ending to 2017 I wanted. Since then I had to accept the cards I had been dealt, remain positive and focus on factors which are within my control; rehabilitation and rescheduling the fight.
“Over the past five years, I’ve had a number of challenges to overcome, but learnt often during times of adversity we learn and grow. As a result, come May 5, Tony will be faced with a more experienced and more determined opponent.”
A fight between Bellew and Tyson Fury was mooted but the Liverpudlian has stuck to his side of the bargain to fight Haye.
As for Haye, UFC star Jimi Manuwa called out the boxer for a fight next summer.
“I think everyone knows of my feud with David Haye,” Manuwa said.
“I think he is the perfect candidate for me to cross over to boxing.”