The bout between Fury and Paul was originally scheduled for December 2021 but the Briton called it off, saying he had a chest infection and broken rib.
After a long-running online feud between the pair, the lucrative fight has been criticised because of their novice records.
Fury previously said he only took the fight to make money and that a victory would have given him "no credit in the boxing world".
American Paul has a record of five wins as a professional, against fellow social media star AnEsonGib, ex-NBA basketballer Nate Robinson and mixed martial arts fighters Ben Askren and Tyron Woodley.
Meanwhile, Fury - the half-brother of WBC world heavyweight champion Tyson - has eight professional victories in his career and found fame on the reality TV series Love Island.