But Wilder's team won an arbitration hearing which stated that the he had the right for a third fight, now set for July 24, with Las Vegas' Allegiant Stadium the tipped venue.
Fury, who was in Las Vegas to see Scot Josh Taylor beat Jose Ramirez, signed the Wilder contract and said: "Shall we do it and put him out of his misery?
"Crack the other side of his skull? Give him another shoulder injury, another bicep injury, a leg injury... the whole lot.
"Wilder, contract's signed, you're getting smashed. When I say smashed, I mean smash, smash, smash.
"You're getting knocked out, end of, one round, you're going, I've got your soul, your mojo, everything. I own you."
Fury first took on the then-defending WBC heavyweight champion in Los Angeles in 2018, with the Bronze Bomber retaining his strap after a controversial split decision draw.
MGM Grand Garden Arena hosted the rematch in 2020 with Fury taking the title with a seventh round TKO.
Joshua has been ordered to defend his WBO heavyweight title against mandatory challenger Oleksandr Usyk.
Additional reporting by Press Association.