Texas Tech made the announcement after holding a team meeting to inform the players of Wells' hiring. He replaces Kliff Kingsbury, who was fired Sunday after a 5-7 season.
"Quickly in the interview process, it became clear Matt Wells and his leadership style were a perfect fit to lead our football program," Texas Tech athletic director Kirby Hocutt said in a statement. "We have a great future in store under Coach Wells, and I firmly believe he is the right coach to take us to an elite level. We are thrilled to welcome Coach Wells and his family to Lubbock."
A news conference to introduce Wells in scheduled for Saturday.
Wells, 45, was 44-34 in six seasons at Utah State. The Aggies went 10-2 this season, and Wells was named coach of the year in the Mountain West Conference for a second time.
Wells will bring Utah State offensive coordinator David Yost and defensive coordinator Keith Patterson with him to Lubbock.
"I am excited to meet the team and get to work on building an elite program that Red Raider fans will enjoy every Saturday," said Wells, an Oklahoma native who also has served as an assistant at Navy, Tulsa, New Mexico and Louisville.