The pair were originally set to fight on December 17, only for Haye to have to pull out due to what he described as a "freak accident" which saw him damage his bicep in training.
Bellew won their previous bout in March but his rival's Achilles injury, that he appeared to aggravate in the ring, meant there were immediate calls for them to renew hostilities at a later date.
A new date has now been set and the 'Bomber' says he is desperate to make Haye pay when they step back into the ring, admitting the news has derailed his Christmas plans.
"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," Bellew told Sky Sports.
"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 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."