1024 GMT August 21, 2019
Britain's Fury and American Wilder shared a controversial and thrilling draw in Los Angeles on December 1, BBC Sport reported.
Both fighters have said they want a rematch, while Fury is pushing for it to be in the UK.
The WBC said in a statement there was a "unanimous agreement" to sanction a rematch in a meeting of the board of governors.
"Wilder and Fury gave boxing one of the best fights in the heavyweight division in a long time, which has created tremendous popular demand for the fans to see a rematch," it said.
"The WBC is happy to confirm a direct rematch has been approved."
Wilder's mandatory challenger is Dominic Breazeale but this decision by the WBC clears the way for him to fight Fury again next without being stripped of his belt.
Although Fury was knocked down in the ninth and 12th rounds, many observers thought the 30-year-old Briton should have won the bout, which was scored 115-111 for Wilder, 114-112 for Fury and 113-113.
Fury's promoter Frank Warren said he and the British Boxing Board of Control would write to the WBC demanding another bout and asking for an explanation of the scoring, with Mexican judge Alejandro Rochin having awarded Wilder seven of the 12 rounds.
Fury said he had "never seen a worse decision in my life" and described it as a "gift" for his opponent.
In an Instagram post in response, Wilder, 33, said, "You saw the best Fury but you did not get the best Wilder and I still managed to get the job done."
Wilder also questioned if referee Jack Reiss' count was too slow in Fury's remarkable rise from the canvas in the 12th round, which Reiss denied.