Joshua, 34, had previously described a potential bout with Cameroon-born Ngannou as a "gimmick fight".
The 37-year-old former UFC champion only made his professional boxing debut in October, when he knocked down Tyson Fury before losing a close decision.
Joshua and Ngannou will meet at a news conference on Monday evening in London.
Former UFC heavyweight king Ngannou stunned the boxing world last year when he sent the undefeated Fury to the canvas with a left hook.
The 35-year-old Briton, who recovered to win the 10-round bout by split decision, will fight Oleksandr Usyk on 17 February for the right to become the first undisputed heavyweight champion since 1999.
Fury is the WBC champion, with Ukraine's Usyk, 36, holding the WBA, WBO and IBF belts.
Saudi organisers were intent on hosting Joshua v Deontay Wilder on 9 March, but the American's points defeat by Joseph Parker on 23 December scuppered those plans.
Joshua stopped Otto Wallin on the same card and organisers were determined to find a bout for the Watford fighter on the same weekend the Wilder showdown had been pencilled in for.
Joshua v Ngannou will take place on a Friday to avoid a clash with the Saudi Arabian Grand Prix which is due to be held in Jeddah on Saturday, 9 March.
Why is Joshua fighting Ngannou?
Just a few weeks ago Joshua was downplaying the prospect of fighting boxing newcomer Ngannou, but Wilder's defeat by Parker forced him to rethink his plans.
As well as that, Joshua is keen to put himself in the mix to face the winner of Fury v Usyk or potentially fight for the IBF title should it become vacant following the undisputed bout.
Despite majorly troubling Fury, Ngannou will be a big underdog against Joshua, who has twice held world heavyweight titles.
The fight represents less risk for Joshua than might be anticipated against a seasoned heavyweight like Parker - who many might have considered an obvious choice after his victory over Wilder.
Fighting Ngannou can keep Joshua ticking over while at the same time keeping the Saudi organisers happy as they get to close 'Riyadh Season' with another heavyweight event.
Saudi Arabia has ploughed millions of dollars into staging huge sporting events, with critics saying the unprecedented spending is being used to enhance the oil-producing kingdom's international reputation and deflect from its human rights record and environmental impact.
However, in a recent interview with the BBC, Saudi Arabia's sports minister Prince Abdulaziz bin Turki Al Faisal said claims of 'sportswashing' were "very shallow", insisting the investment is boosting the country's economy, opening it up to tourism and inspiring people to be more active.
<p> </p> <div data-testid="westminster"> <div data-testid="card-text-wrapper"> <p data-testid="card-description">The foreign secretary's remarks come as the government...