The show will begin production Nov. 30 "with a series of interim hosts from the Jeopardy! family" beginning with Jennings -- the record holder for most consecutive games won in the show's history at 74.
"Alex believed in the importance of Jeopardy! and always said that he wanted the show to go on after him," executive producer Mike Richards said. "We will honor his legacy by continuing to produce the game he loved."
Trebek, who hosted the game show for 37 years, died on Nov. 8 following a battle with pancreatic cancer.
"There will only ever be one Alex Trebek, but I'm honored to be helping Jeopardy! out with this in January," Jennings wrote on Twitter following the news that he would host the show.
Jennings joined the show as a consulting producer in September, presenting his own special video categories.
He also won the Jeopardy!: The Greatest of All Time competition in January.
Jeopardy! also announced that the final week of episodes hosted by Trebek will air on Jan. 4, preceded by 10 of his best episodes in the weeks of Dec. 21 and Dec. 28.