WASHINGTON—President Trump endorsed former football coach Tommy Tuberville in the runoff to be the Republican nominee for the U.S. Senate in Alabama, throwing his influence behind the opponent of his former attorney general, Jeff Sessions, who is trying to win back his old seat.

“Tommy was a terrific head football coach at Auburn University,” Mr. Trump wrote in tweets late Tuesday. “He is a REAL LEADER who will never let MAGA/KAG, or our Country, down! ... Coach Tommy Tuberville, a winner, has my Complete and Total Endorsement,”...