Joshua added the WBA heavyweight title to his IBF belt with a thrilling knockout victory over Wladimir Klitschko in 11 rounds at Wembley Stadium on Saturday night. On the line is Joshua's IBF title, as well as the vacant WBA and IBO belts.
Fury has been inactive since his defeat of Klitschko having most recently struggled with depression, but has made plenty of noise on social media in the run up to the fight having returned to training in Marbella.
The fifth round, in particular, was action-packed.
The Ukrainian legend kept Joshua at bay with probing jabs in the first and stunned him with a stinging right hand in the fourth.
Fury responded to the challenge on Twitter, writing: "Well done Anthony Joshua good fight, you had life and death with Klitschko and I played with the guy, let's dance".
The rookie mistake allowed Klitschko to rally, almost taking the lead as the two 6-foot-6 men went to the 11th round - four rounds longer than any Joshua fight had ever gone.
Wladimir Klitschko has expressed his interest in an immediate rematch with Anthony Joshua after suffering a dramatic 11th-round stoppage defeat at Wembley Stadium on Saturday. Though he made it to his feet, Joshua immediately pounced and referee David Fields stepped in and called the fight.
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"I was planning to do it, it didn't work".
"As boxing states, you leave your ego at the door and you respect your opponent", Joshua later added. He looked to be overmatched in the early rounds, but fought his best after he was knocked down. "He's a role model in the ring".
Klitschko, 41, fell to 64-5 in a long career that began in 1996 after he won the Olympic gold in Atlanta.
According to kwese Sports, the viewing party erupted anytime Joshua knocked out his Ukrainian opponent.
Joshua weighed in at 250.1 pounds, while Klitschko weighed in at 240.5 pounds.
In the end it was Joshua who announced himself as the future of the division. "19-0, three and a half years in the game", said Joshua.
"Tyson Fury, where (are) you at baby?" asks Joshua. "I came back and I fought my heart out, that's what I'm about". As I'm thinking about the fight and it's still fresh, I'm actually taking down notes of little things of how I can improve.