Joshua had announced plans to face ex-WBC champion Deontay Wilder if they had both won while fighting on the same card in Riyadh on December 23.
However, Wilder was handed a stunning upset defeat by New Zealand's Joseph Parker last month, before Joshua clinched a knockout win over Otto Wallin later that night.
"Tonight we confirm it's a Done Deal," Joshua's promoter Eddie Hearn on Friday said in a post on social media platform X, formerly known as Twitter.
"Anthony Joshua v Francis Ngannou collide on a huge night in Riyadh, Saudi Arabia - press conference Jan 15 in London with full details dropping soon!"
ESPN reported the fight would be held in early March, weeks after WBC world champion Tyson Fury faces WBA, WBO, IBF and IBO champion Oleksandr Usyk for the undisputed heavyweight championship of the world.
Ngannou, who vacated his heavyweight belt after a contract dispute with UFC and exited as a free agent in January last year, made his pro boxing debut against Fury in October.
The Cameroonian-French fighter lost on a split decision in the non-title fight, but almost delivered an upset when he dropped Fury to the canvas with a left hook.
Following his loss to Fury, Ngannou was ranked number 10 in the heavyweight division by the World Boxing Council (WBC).
