Cumbie has been Texas Tech's offensive coordinator but took over as interim head coach after the school fired Matt Wells on Oct. 25.
New Red Raiders coach Joey McGuire retained Cumbie as offensive coordinator, but Cumbie instead will go to Louisiana Tech, which has scheduled an introductory news conference for Wednesday.
Cumbie, 40, replaces Skip Holtz, who is out following nine seasons and a 64-50 record.
A former Texas Tech quarterback, Cumbie returned to his alma mater after the 2020 season as offensive coordinator. He spent the previous seven seasons as an offensive coordinator and quarterbacks coach at TCU. Cumbie, who played briefly in the NFL and Arena League, also worked as an assistant for Texas Tech from 2011 to 2013.
Texas Tech announced Tuesday night that Cumbie will still coach the Red Raiders in their upcoming bowl game. Athletic director Kirby Hocutt has asked all of the team's remaining assistant coaches to work through the bowl game, too.
"I'd like to personally congratulate Sonny Cumbie on being named the next head coach at Louisiana Tech," Hocutt said in a statement. "I think anyone that knows Sonny can feel the passion and love he has for Texas Tech University and West Texas, and he brought that every day this past year as our offensive coordinator and most recently as our interim head coach.
"Make no mistake, we intend to compete and win whatever bowl game we are selected for later this week. For that to happen, I feel it is in the best interest of our student-athletes for Coach Cumbie to return and lead our team one final time."