A deal was agreed to after the British fighter watched the Ukrainian's brother, Wladimir, retain his IBF and WBO heavyweight belts by stopping Hasim Rahman in the seventh round on Saturday.
"I was out in Germany to watch Wladimir Klitschko bore everybody to sleep with his jab," Haye told the BBC Sunday. "It's all done and dusted; just need to dot the i's and cross the t's.
"We sat down and talked numbers and that made sense for both sides and it's done. There is no boxing politics involved. Plain and simple, this is how boxing should be."
Last month, Haye won a five-round TKO over Monte Barrett in his first fight since moving up to the weight. He had unified the cruiserweight titles before moving up a division to floor Barrett five times in five rounds.
Vitaly Klitschko watched Haye show his full range of shots at London's O2 Arena, which could be the venue in June.