Former UFC heavyweight champion Ngannou, 36, has no professional record in boxing.
Team Fury say the fight is not an exhibition and will “take place under the official rules of professional boxing, with three judges ringside adopting the 10-point must system”.
Fury will not be defending his WBC title in the Riyadh bout.
“This guy is supposed to be the hardest puncher in the world, but let’s see how he reacts when he gets hit by the Big GK,” Fury said, referring to his ‘Gypsy King’ nickname.
Ngannou said it was a dream come true to box Fury.
“I’ve been waiting to meet Tyson in the ring for the past three years,” he said.
“All I will say to Tyson for now is he better dance in that ring because if I touch him, he’s going to sleep.”
The WBC said it would not be involved in the fight but had granted Fury “special permission” to compete in a non-title bout as he has no pending mandatory challenger in place.
Fury has gone with a left-field option after failing to agree terms with Oleksandr Usyk over an undisputed fight earlier this year.
Fury’s co-promoter Frank Warren also suggested that fight is unlikely to happen in 2023 after Usyk signed with Saudi Arabia’s Skill Challenge Promotions.
“They’re saying that will be in February next year,” Warren said of Team Usyk.
“If everyone were to sit around waiting for them we’d have a problem. We’re not sitting about, we’re getting on with it.”
Ukrainian Usyk is set to defend his titles against his WBA mandatory challenger Daniel Dubois in August and had hoped to fight Fury in December.
Fury has faced criticism for failing to reach terms with Usyk and his choice of opponent, but Warren said the 34-year-old was not avoiding any fighter.
“For anyone to talk about Tyson ducking anyone is absolutely beyond ridiculous,” Warren said.
“Because he’s the best heavyweight of his generation. None of them, and I represent interim champions and those fighting for world titles... Tyson is the best of his generation at this moment in time.”
Ngannou held ambitions of being a boxer early in his career before focusing his full attention on MMA.
“This is my opportunity to make that dream come true and cement my position as the baddest man on the planet,” he said.