Fury had just whitewashed Francesco Pianeta by winning every round at Windsor Park in Belfast.
Wilder, who was a special guest commentator for BT Sport, stepped into the ring and shouted into the mic that "it's on, it's official".
"It's what we have been waiting for, the best versus the best," Wilder added.
Promoter Frank Warren said the exact date and location had yet to be decided, but Fury forgot about that, and gave the game away.
He said: " Now he gets the chance to fight the Lineal champ.
"One thing I promise when I go to Las Vegas is I am knocking you the f*** out boy."
Fury also couldn't resist taking a shot at rival Anthony Joshua after his failed attempts to land a fight with Wilder.
He said: "This man (Wilder) has been trying to make a big fight out of the other chump.
"I think we all know who we are talking about – the biggest s***house in boxing."
Fury then paid tribute to Belfast, promising the Northern Irish city that he would win the WBC belt for them and defend it back there.
He added: "Belfast you are beautiful. It's like a homecoming for the Gypsy King.
"I promise you I am taking to the WBC title and I will take it back and defend right here in Belfast."
Wilder responded: "Sorry to tell you, Tyson Fury will not be bringing the belt back here."
Despite his wide-margin points win against Pianeta, Wilder will have taken heart that Fury didn't get the huge outsider out of there after 10 rounds.
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