Promoter Eddie Hearn has confirmed to ESPN that rival world heavyweight champions Anthony Joshua and Tyson Fury "have agreed the basics of the deal" to fight two times in 2021.
ESPN understands there is an agreement -- but no signed contract yet -- for a 50-50 split from both sides, with the first fight likely to happen in the summer of 2021.
Venues and dates have yet to be agreed while both English boxers also have defences of their titles to get through for their two fights to happen.
"We have agreed the basics of the deal, a two-fight deal," Hearn, who promotes Joshua, told ESPN.
"The hardest part is to agree financial element of the deal. We have agreed with Tyson Fury and the team and we can now move forward with finalising the smaller parts of the deal. The good news for fight fans is that we have agreed to do the two fights and we can now go and dot the i's and cross the t's.
"They also have fights in between to make and get through, and that's another issue."
Fury (30-0-1, 21 KOs), 31, from Manchester, England is due to face American Deontay Wilder later this year in a third fight after he stopped Wilder (42-1-1, 41 KOs) in the seventh round in February following a controversial draw in December 2018.
Joshua (23-1, 21 KOs), 30, from Watford, England holds the other world heavyweight titles (IBF, WBA and WBO) and is due to face Bulgaria's Kubrat Pulev next. Hearn is working on where and when that fight takes place but at the moment there is no news on when sport can take place in front of crowds again in the UK due to restrictions over coronavirus.
Fury is also due to face another Briton Dillian Whyte in a mandatory defence early in 2021.
"Who knows what's going to happen with Deontay Wilder but we [Matchroom Sport] want Dillian Whyte to fight for the world title and he is supposed to fight Tyson Fury, the WBC champion, by February 2021," Hearn said.
"There are obstacles to overcome but the god news is that we are moving forward."
Fury also took to social media to confirm the fight.
"The biggest fight in British boxing history has just been agreed. Two fight deal, Tyson Fury v AJ next year. One problem: I have to smash Deontay Wilder's face right in, then we go into the Joshua fight next year," he said on Twitter.
Hearn said Fury-Joshua for all four world heavyweight titles would be the biggest fight in British boxing history and set pay-per-view records in the UK.
"It's probably the biggest fight of all time for British sport, there has been nothing to compare it to and there never will be again," he added.
"It's colossal and everyone is moving in the right direction. A lot of it [revenue] is pay-per-view led. From a British point of view, this will do over two million pay per view buys in the UK, it's not so big in the US."
Fury-Joshua would attract a 90,000 crowd to a venue like Wembley Stadium in London in the summer of 2021, but Hearn said other nations will also be considered to host the fight if it happens.
"It's too early to say where it could take place, it's two Brits and obviously it makes sense to have it here but a lot of other countries want to stage this fight and we will look at it."
"It is two Brits but there's much more money available. Middle East will want to stage it and will make a huge play to stage it there. They have both fought in Saudi Arabia -- Tyson did WWE there, and AJ had his last fight there [December, 2019]. Las Vegas will go after it and we have already had approaches from China to stage it there."
Frank Warren, who co-promotes Fury along with Top Rank's Bob Arum, confirmed to ESPN a 50-50 split has been agreed, but downplayed the significance of Hearn's comments and insisted no contract had been signed.
"It was always going to be a 50-50 deal and a rematch. Other than that nothing has been agreed, no contract," Warren told ESPN.
"It's looking like Wilder [as Fury's next fight] towards the end of the year unless something comes up.
"I hope the Joshua fight happens and I would like it this year if we can.
"These guys [Fury, Joshua] could get between $60 to $70m each from one fight against each other, double that if there's a rematch, in one year."