The blockbuster all-British bout between WBC champion Fury and Joshua, who holds the IBF, WBO and WBA titles – will be the first time all four belts have been on the line in the heavyweight division.
Fury's promotor Arum confirmed that his fighter and Joshua are now in the process of putting pen to paper to confirm the contest.
Arum told iFL TV: "As far as I'm concerned, I've been working on it, and all the points have been agreed.
"That's what each side has said. Now, we are scrambling around to get the thing signed and everything.
"But I can say clearly, based on my view on everything, that there are no more issues."
As things stand no venue or date for the bout has been confirmed.
History in the making
Finally, boxing gets what it needs in Joshua vs Fury.
Negotiations haven't been plain-sailing but it will be a fight which captures the imagination of the UK in particular with it being the first all-British showdown for all four major world titles.
Fury is an early favourite with Paddy Power at 4/7 while Joshua is 11/8. For an unlikely draw, which would guarantee fans getting a rematch, you can get odds of 22/1.
Fury is 15/8 to win by decision and 9/4 to win by KO. AJ, meanwhile, is 11/2 to earn a verdict on the cards and 5/2 for inside the distance.
Joshua most recently fought in December, defeating Kubrat Pulev to make the first defence of his second reign as unified champion.
In unfamiliar circumstances, Joshua fought in front of 1,000 fans at the SSE Arena in Wembley, London due to the Coronavirus pandemic.
Despite it being a smaller occasion than normal, Joshua returned to his best by delivering a ruthless knockout of Pulev in round nine. It was the first time he had fought since outpointing Andy Ruiz Jr. in December 2019.
The "Gypsy King" has not laced up a pair of gloves since demolishing Deontay Wilder in February 2020.
Fury, fighting the American in a much-anticipated rematch, stunned a sold-out MGM Grand Arena to snatch away the WBC crown from Wilder.
In doing so, he became just the second fighter to have won every major world title after Riddick Bowe.
Britain's biggest fight in boxing history is expected to take place in the Middle East and is projected to generate two million pay-per-view sales in the UK.