Britain's Fury is the WBC world champion while Ukrainian Usyk holds the WBA, WBO, IBF and IBO belts.
Talks for a blockbuster unification title fight were revived after breaking down months ago and organisers said it would be promoted by Queensbury Promotions, Top Rank, K2 and Usyk17 at Riyadh's Kingdom Arena.
"You can't run rabbit run anymore Usyk, you're getting it," Fury wrote on Instagram.
Heavyweight boxing's last undisputed champion was Britain's Lennox Lewis in 1999.
"This is the fight that everyone has wanted to see for some time and now it is finally happening - the world's two heavyweight champions going into the ring against one another," said Turki Alalshikh, chairman of Saudi Arabia's General Entertainment Authority, in a statement.
"It is the biggest fight in boxing, the world will be watching, and we are so proud to be the hosts for this spectacle as part of the fourth edition of our Riyadh Season celebrations."
