After negotiations seemingly stalled for the bout, which would decide the first undisputed heavyweight champion since Lennox Lewis, it was expected that both Joshua and Wilder would go down the route of mandatory defences in the autumn.
A rematch is also included as part of initial fight deal, ending months of speculation as to whether the unbeaten heavyweights would lock horns.
ESPN's Dan Rafael later quoted Shelly Finkel, Wilder's co-manager, as saying that the Wilder camp had agreed to terms with Joshua manager Eddie Hearn on a fight in the United Kingdom this fall, possibly as early as mid-September.
Wilder posted on Monday night: 'The $50M offer for Joshua to fight me next in the U.S. is still available to him if he wants it.More news: May strikes deal with pro-EU rebels ahead of crunch Brexit votes
Wilder had previously attempted to lure Joshua to fight in the United States with a $50m offer, but Joshua and Hearn have been firm in their stance that the match-up should happen in Britain.
"There's no [percentage] split, but they've offered us a good purse".
Joshua and promoter Eddie Hearn have yet to publicly respond, though Hearn has previously criticised the Wilder team for appearing to do their business via social media, insisting "deals are made in the boardroom, not on Instagram".
"I don't think they are too keen to do the fight in the U.K.", Hearn told Sky Sports last week.More news: E3 2018: Star Fox and Starlink Crossover Announced at Ubisoft E3 Event
The fight is pencilled in for February 2019.
"We have agreed to the terms that Eddie has put out to us for a fight in the UK", Wilder was quoted by ESPN as saying.
'If for any reason Anthony changes his mind and wants to fight in the U.S, the $50m offer we have made to him is still there. Not as good as we feel it should be, but we want the fight and we're willing to take what they offered.More news: NYCFC hires Man City assistant to replace Vieira
He said on Instagram: 'Dear Anthony Joshua fans, since your acting dumb, delusional or just plain Stupid here you go, breaking news.
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