England's Joshua wants to fight Wilder at Wembley Stadium, which has a retractable roof.
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.
"We have agreed to the terms that Eddie has put out to us for a fight in the U.K.", Finkel told ESPN.
According to Pugmire, Wilder's and Joshua's respective teams were quibbling over the location of the fight, with Wilder's camp wanting it in the US and Joshua's side preferring the UK.
"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", Finkel said.
The location had proved to be one of the main issues in negotiating the fight over the past two months; Wilder's team offered Joshua a reported $50m (£37m) to fight in the U.S. but the 28-year-old Briton has remained adamant he wants to fight in the UK. "Deontay wrote to Joshua and said 'Hey, I accept your offer, let's fight in the U.K'".More news: Phillies poke fun at IHOP with ridiculous name change
Hearn has already stated that a mandatory challenge against Alexander Povetkin could be next with Wilder straight after, but the American's concession may have ripped up the plan. "Not as good as we feel it should be, but we want the fight, and we're willing to take what they offered", Finkel said.
'We will wait and see what happens when we get the contract back. Hopefully, we'll get an answer in the next day or two.
"We're going to dealing with that and making sure he gets the relevant paperwork".
Undefeated Wilder (40-0, 39 KO's) agreed to the two-fight deal, with the first bout to take place in the United Kingdom. "It's up to them to choose".
Another possible outlet is the Perform Group's DAZN sports streaming service, which is due to launch in the USA later this summer, with Hearn's recently agreed to eight-year, $1 billion deal to provide boxing content due to begin in September.
Should Joshua, 28, fight the American next, the victor would become the first heavyweight to hold all four recognised world titles at once. I think from Deontay Wilder's messages on social media, he seems fine with that.