Britain's Joshua, the former WBA, IBF and WBO champion, will take on Sweden's Otto Wallin while American Wilder, the former WBC champion, faces New Zealand's Joseph Parker at Riyadh's Kingdom Arena.
Parker is also a former WBO champion.
Joshua and Wilder could fight each other next year if both win in Riyadh.
The December 23rd show will also feature two world title clashes, with WBA light-heavyweight champion Dmitry Bivol scheduled to fight Britain's Lyndon Arthur while Australian WBC cruiserweight champion Jai Opetaia takes on Britain's Ellis Zorro.
British heavyweight Daniel Dubois, who lost to WBA, IBF and WBO champion Oleksandr Usyk in Poland in August, will be back in the ring to fight undefeated American Jarrell Miller.
Ukrainian Usyk had been due to fight WBC champion Tyson Fury for the undisputed crown in Riyadh on December 23rd but that has been put back to give the Briton more time after a bruising non-title fight with Francis Ngannou.
A date for that fight is due to be announced on Thursday, with February looking likely.
Joshua told reporters last month that a fight between him and Wilder could be staged on the undercard of the Usyk vs Fury clash.
Matchroom Boxing's Eddie Hearn said the Riyadh show, led by Queensberry Promotions' Frank Warren, had come together in record time thanks to the Saudi authorities.
"This is the fastest I've ever seen a fight card come together," Hearn told a London news conference.
"We're talking about conversations that started 10 days ago, max, and that wasn't even necessarily AJ (Joshua) at the time. That was Dmitry Bivol, that was Jai Opetaia and then it went into AJ.
"I've never seen anything like it. I think the speed of it actually benefited everybody because no one really had time to fall out."
