The Gypsy King put on an incredible show as he saw off Deontay Wilder in seven rounds to win the WBC heavyweight title.
The other belts are held by AJ, whose next fight is lined up against Bulgarian fighter Kubrat Pulev.
Talk quickly turned to a bout between the pair after Fury’s win in Las Vegas on Saturday.
And Hearn, who has been working with the four-belt champion throughout his career, gave an update.
Speaking on Sky Sports New , the promoter said: “I promise you this fight will happen.
“If we have to fight Pulev, we've got to beat Pulev, and if he has to fight Wilder, he's got to beat Wilder again.
“Both of those things will happen.
“Fury will beat Wilder again and Wilder will knock Pulev clean out, despite Bob Arum telling us very differently.
"You will get this fight. We will do everything that it takes to make this fight."
The promoter went on to explain how a fight between the Brits could be organised.
"He's promoted by Bob Arum predominantly,” Hearn added.
“Frank Warren is also involved, MTK are his management company.
“I’ve spoken to Top Rank and I've spoke to MTK straight after the fight.
"Everybody is very clear on this. Everybody wants this fight - Anthony Joshua, Tyson Fury, MTK, Top Rank, Frank Warren, Matchroom.
"There are some hurdles to overcome on the broadcasting, but nothing too much.”
Hearn tweeted about a fight between the pair within minutes of Fury’s win on Sunday morning.
"Wow unbelievable from Fury! Fair play and well done Sugar Hill and Andy Lee on first class game plan,” Hearn initially tweeted.
Then asked on social media whether he would be letting Joshua near Fury after his brilliant display in Las Vegas, Hearn replied: “Of course I am! And AJ wants it bad..this fight is gonna and has to happen this year!”