Former cruiserweight world champion Bellew and ex-heavyweight title holder Haye had been due to renew their rivalry on December 17, only for the fight to be postponed after the latter tore his bicep in an accident on a stairwell.
Bellew claimed a stunning victory in their first meeting on March 4, defying the odds as Haye was rendered immobile by an ankle injury, leading his corner to throw in the towel in the 11th round.
In a statement, Bellew expressed his desire to end Haye's career and then take on another former world heavyweight champion in Tyson Fury, who has not fought since defeating Wladimir Klitschko in November 2015.
"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 said.
"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 Fury and end both their careers but first things 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."
— Matchroom Boxing (@MatchroomBoxing) December 5, 2017
Haye added: "Whilst the first chapter of the Haye-Bellew saga didn't go my way, fans were left on the edge of their seats throughout the thrilling 11-round battle.
"The rematch in May will no doubt eclipse this, Tony has boasted that the rematch gives him the opportunity to force me into retirement. Unquestionably, I step into the ring on 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, Tony will be faced with a more experienced and more determined opponent."
Photo by: Getty Image. Caption: WBC Cruiserweight champion Tony Bellew in his fight with David Haye