The two heavyweights clashed in December, where the bout ended as a controversial draw.
Boxing fans will hope that the victor will then take on the victor of Fury vs Wilder 2 in a fight by the end of the year that could be one of the biggest fights in boxing history.
"I'm delighted that Frank [Warren] and Queensberry Promotions have teamed up with Top Rank to promote my fights in America", Fury said in a statement.
But Fury's December draw with Wilder aired on BT Sport in the United Kingdom as well as Showtime - who broadcast Wilder's fights - in the US.
The Wilder-Fury fight did 320,000 on pay-per-view in the US and approximately 400,000 in the U.K. It is expected that number could rise, perhaps significantly, for a rematch given the way the first bout ended. "With ESPN and BT Sport behind me, the biggest sports platforms in the world are now linked up with the best heavyweight in the world!" In fact, a purse bid ordered by the WBC was twice postponed due to the fact that a deal was so close.
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Now Fury has his own U.S. broadcaster, agreements will have to be reached between ESPN and Showtime over the airing of his fights in America. But the biggest fights in the division now look very complicated to make. But his much-publicized downward spiral into depression, drug abuse and obesity saw him vacate his trio of world titles.
A bout that would see a true undisputed heavyweight champion of the world crowned and one that would settle this Joshua, Fury and Wilder debate once and for all.
Previously, Fury's lack of a permanent US television home made it feel like any fight was possible.
'They could have got the fight but they did not take advantage of their position. "It's a different situation now, Showtime's not the only game in town, it's changed dramatically and it's up to us now to sit down and get it over the line", he said.
Joshua makes own U.S. bow on June 1 at New York's fabled Madison Square Garden against the undefeated Jarrell Miller.