The fight, which has been discussed for more than a decade, will be broadcast globally on Netflix. Organisers are also considering a late start time to accommodate viewers in the United States, meaning the main event could take place during the early hours of Saturday morning in the UK.
Joshua, 36, and Fury, 38, are expected to begin their official promotional build-up at a news conference in London on Wednesday, 30 September. Joshua marked the announcement on Instagram by writing, "I am inspiring a generation," while Fury had yet to publicly comment.
The event is being promoted through a partnership involving Saudi boxing figure Turki Alalshikh's The Ring and UFC president Dana White.
"Two of the best heavyweights of this generation, finally in the ring together," Alalshikh said, describing the contest as one of the biggest fights in boxing history.
The former two-time world champions had already signed contracts earlier this year, but organisers had not confirmed a date or location. Wembley Stadium in London and Madison Square Garden in New York had been considered, although both venues presented challenges before Cardiff became the preferred option.
The Principality Stadium has previously hosted major boxing events, including Joe Calzaghe's 2007 victory over Mikkel Kessler, which began at 01:00 GMT to accommodate American television audiences.
Officials from the Welsh Rugby Union and Cardiff Council welcomed the announcement, saying the event could strengthen Cardiff's reputation as a major sporting destination and provide a significant boost to the local economy.
Joshua had pushed for the fight to be held in Britain, and promoter Eddie Hearn said the support of UK fans had been important in getting the contest over the line.
White's involvement adds another major name to the promotion. He said Joshua and Fury bring a combined 66 victories, 52 knockouts and multiple heavyweight world titles into the ring.
The exact fight time has not yet been confirmed. However, there is a history of major British boxing events starting late to suit American broadcasters. Previous examples include Ricky Hatton's 2005 fight with Kostya Tszyu and Calzaghe's bouts against Jeff Lacy and Mikkel Kessler.
After years of failed negotiations, Fury and Joshua finally have a confirmed date and venue for their long-awaited showdown.
