Wilder, 38-0 with 37 knockouts, was due to face Luis Ortiz, but the Cuban southpaw tested positive for banned diuretics often used as steroid masking agents, becoming the third Wilder challenger in the past 18 months to test positive and scupper a planned title bout for the American.
Stiverne, 25-2 with one drawn and 21 knockouts, was on the undercard but will move into the main event on the November 4 event at Brooklyn's Barclays Center.
"Stiverne will pay for Luis Ortiz screwing up," Wilder said.
A victory for Wilder could set the stage for a 2018 unification showdown against the reigning International Boxing Federation and World Boxing Association champion Anthony Joshua, who is 19-0 with every win by knockout.
"Despite all of these obstacles that are thrown in my path, it still will not stop me from reaching my ultimate goal, which is to be the undisputed heavyweight champion of the world," Wilder said.
Wilder began his reign in January 2015 by taking the WBC crown with a unanimous decision triumph over Stiverne in Las Vegas -- the only fight in Wilder's pro career to go the distance and one where he suffered a broken right hand.
"In the first fight, I broke my hand in the third round and I still dominated. That was a lot of the reason why it went the distance," Wilder said.
"This time it's a different day, different time and different fight. This time it won't end well for him."
Stiverne, the WBC mandatory title challenger who was paid to step aside so Wilder could face Ortiz, was hospitalized after the first fight for severe dehydration and muscle damage.
He has not fought in two years but has pushed for a title rematch.
"Stiverne asked for it, so he's going to get it," Wilder said. "Whatever happens happens. I'm relieved to be getting my mandatory out of the way. At least now I won't have to deal with that down the road."
Stiverne, who was to have faced American Dominic Breazeale, won the WBC crown in 2014 by knocking out American Chris Arreola.
"I am ready, willing and able to seize back my title from Wilder," Stiverne said. "Wilder dodged a bullet in the first fight, but not this time. It was my fault, but I learn from my mistakes."
It will be the sixth title defense for Wilder, who saw a scheduled May 2016 bout in Moscow against Russian Alexander Povetkin and a planned bout last February in his home region at Birmingham, Alabama, against Poland's Andrzej Wawrzyk both implode after his rivals failed doping tests.
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