Bellew defeated Isaac Chilemba, at the second time of asking after their first bout had ended in a draw, in a final eliminator back in May to become the mandatory challenger for the crown.
At that time Chad Dawson was the reigning champion, but the American saw it slip from his grasp in June when he was stopped inside a round by Stevenson.
The new title holder has requested an interim bout against former IBF champion Tavoris Cloud in September, but the WBC will only let that happen if Bellew then gets to take on the winner within 90 days.
Liverpudlian Bellew has challenged for a world title once before - back in 2011 when he was out-pointed by Welshman Nathan Cleverley in his attempt to be crowned WBO champion.
Since then he has won four of his five bouts, the other being a draw against the tricky Chilemba in his home city.
Stevenson has a professional record of 21-1, the Canadian's only defeat coming at the hands of Darnell Boone three years ago. He avenged that loss earlier this year before going on to knock out Dawson in Montreal.