Britain's Fury roared out a challenge to Ukrainian Usyk, the WBA, IBF, WBO and IBO champion, after retaining his WBC title this month with a 10th-round stoppage of compatriot Derek Chisora.
The exact date and location for the unification showdown have yet to be finalised. Neither fighter would take a bout before their face-off, Arum said.
"The two fighters have agreed to fight each other next," Arum told Sky Sports on Tuesday.
"Usyk is a good friend of mine, he's very intelligent and Tyson is Superman, both as an athlete and as an intellect. So they want the fight."
Arum said the promoters had received significant offers from the Middle East to host the fight, while there is also a possibility of the bout taking place in the United Kingdom.
"It shouldn't be too long before a final decision is made. We'll have it all sorted out," Arum said. "I hope maybe by the end of the year."
