American Wilder, 32, and Fury, 30, have agreed to the bout with a venue in the United States, expected to be Las Vegas, set to be announced next week.
The promotional tour for the fight gets under way in London on October 1.
It will be only the third fight of Fury’s comeback – after defeating Sefer Seferi and Francesco Pianeta – following a two-and-a-half-year absence.
Wilder will have held the WBC title for almost four years when he meets Fury, with both fighters boasting undefeated records.
“Deontay Wilder, you are going to get it and you are in big trouble,” Fury said in a video uploaded to his Instagram account.
“I have never met a man I couldn’t beat in the boxing ring or outside on the street.
“I know you have got a big punch and I know you are unbeaten. I know you have got a big mouth and I know you want to win, but you don’t want it like I do.
“You can’t beat me. I will force my will upon you until you quit, and that is a promise.”
Wilder later posted a video to his Twitter account, saying: “I can’t wait.
“It is going to be an exciting fight, an explosive fight, and one for the legacy. Definitely one for my legacy.
“You’ve got the WBC heavyweight champion of the world versus the lineal champion. It is going to be a pleasure.
“The two best heavyweights, competing against each other, the best fighting the best, and giving the people what they want. This is what we’re doing.”
Joshua defends his WBA, WBO and IBF titles against his unglamorous mandatory challenger at a time when he has already been criticised for not fighting
Tyson Fury or WBC champion Deontay Wilder, his significantly higher-profile rivals.
As Joshua’s trainer Rob McCracken acknowledges, Povetkin regardless represents a threat, but the champion’s fellow Matchroom and Sky Sports fighter Bellew completely disapproves because of the Russian’s record of having twice failed drug tests.
The 39-year-old twice tested positive for performance-enhancing drugs in 2016, costing him fights with Wilder and Bermane Stiverne. The WBC also fined him £191,966, but Bellew, its former cruiserweight champion, does not consider that enough.
Bellew, 35 and an increasingly respected figure within his sport, is convinced that the day will come when a fighter who has cheated will kill his opponent, and that largely for that reason those found guilty of doping should never fight again.
“It’s an absolute disgrace that these guys are getting to fight and continue,” he told BBC Radio 5 Live Breakfast. “This is not down to the promoters. This is not down to anyone else but the sanctioning and governing bodies, and it’s an absolute disgrace that these guys are allowed to fight on because it’s going to happen.
“Someone is going to be killed at the hands of a drug cheat. It’s going to be a very, very bad and sad day for boxing when it does, but it will happen eventually. I don’t know when, I don’t know how, but it will, and when it does, I hope that fighter is locked up for the rest of their life because it’s premeditated murder in my opinion.
“I just hope that these sanctioning bodies make some kind of ruling on this before it’s too late.”
By installing Povetkin as Joshua’s mandatory challenger and threatening to strip the champion of his title if he did not defend it against him, it was the WBA who granted the Russian such a lucrative position.
“Giving time served bans is not doing anything,” Bellew added. “Alexander Povetkin should not be even in this fight. It shouldn’t be even taking place.
“I’m pretty sure Anthony Joshua wouldn’t choose to face Alexander Povetkin, and not because he’s scared of him, and not he thinks he’s a brilliant fighter, because Anthony’s shown that he’ll face anybody.
“Why would you want to face a cheat when you don’t have to? You know this man is capable of cheating. He hasn’t just fell by the wayside and made a mistake once. He’s done it twice. It’s not been a one-off mistake.
“When it does happen for a second time, guys should be thrown out of the sport for life. “
Anthony Joshua is feeling under “tons of pressure” as he nears the latest defence of his world heavyweight titles against Alexander Povetkin at Wembley.
The IBF, WBA and WBO champion is returning for the first time to the scene of his finest hour as a professional – last year’s dramatic 11th-round stoppage of Wladimir Klitschko – but does so at a time when he will be harshly judged.
That negotiations for a unification fight with WBC champion Deontay Wilder ended in frustration led to Saturday’s fight with the less-glamorous Povetkin, his mandatory challenger and a significant underdog.
Tyson Fury’s return and swift agreement to a fight with Wilder has also led to wider criticism of Joshua, who in his last title defence against Joseph Parker in March was taken the 12-round distance for the first time.
Against his 39-year-old challenger, anything less than a convincing victory is likely to lead to further criticism, and Joshua said: “There’s loads of pressure; tons of pressure. That’s the reality.
“You’re calm and collected but underneath it all it’s the reality. We both know what we are in for. It’s the same with every fight.
“What more can I do than give my best? I’ll go out there and find a way to win.
“I know I have a lot of fire in my belly; that’s just as important as skills.
“Skills and technique apart, we both have a big heart and can dig deep. We both showed that against Klitschko (who Povetkin lost to on points).
“The one who’s toughest will come out victorious.”
Povetkin, like Joshua an Olympic gold medallist, represents the champion’s toughest fight since that against Klitschko.
He has since overcome Carlos Takam and Parker, when for the first time his performances were criticised, and his trainer Rob McCracken said: “(Povetkin) is a fighter from a different level. With respect to Parker and Takam, Povetkin comes from the top level.”
Similarly to their first press conference, Povetkin was again far smaller than Joshua.
It was a size disadvantage that contributed to his only defeat in 35 fights, by Klitschko in 2013, but he said: “Joshua is one of the strongest in the division.
Anthony is a very strong fighter but I am just as strong.
“When I fought Klitschko I was much weaker and in worse shape than I am now.”