Texas Tech made the announcement Thursday after meeting with players to inform them of the hiring.
Wells 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.”
Texas Tech has scheduled a news conference for Saturday to formally introduce Wells as the new coach.
The 45-year-old Wells has a 44-34 record in six seasons at Utah State.
The Aggies are 10-2 this season, and Wells was named Mountain West Conference coach of the year for a second time.
Wells will bring Utah State offensive coordinator David Yost and defensive coordinator Keith Patterson with him to Texas Tech.
“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, according to ESPN.com.
Utah State will find out Sunday which team it will face for its upcoming bowl game, and it is unknown at this time whether Wells, Yost and Patterson will be on the Aggies’ sidelines for that game.
Kingsbury went 35-40 in six seasons at Texas Tech, his alma mater. He was fired on Nov. 25 and has since been reportedly targeted as the leading candidate for the USC offensive coordinator job.