Theus, 47, who played 13 years in the NBA, has been as assistant under Rick Pitino for the past two seasons.
The Cardinals will play Illinois Saturday in the NCAA Tournament semifinals.
"Reggie will be one of the dynamic coaches in the game," Pitino said. "He has the total package."
Theus, succeeds Hall of Fame Coach Lou Henson, who retired in January.
New Mexico State Athletic Director D. McKinley Boston said that having worked under Pitino Theus "learned from one of the best in the profession, and I think he's going to provide great leadership for our basketball team."