Dykes, who led the nation's top scoring offense at Louisiana Tech this season, replaces Jeff Tedford.
"Sonny Dykes is one of the brightest offensive minds in the country, running a high-octane style of football, one that I'm certain will allow our student-athletes to thrive and that our community will love on game day," Athletic Director Sandy Barbour said.
"However, it was far more than his history of a top-ranked offense and his proven success on the football field that solidified my decision.
"It was the way he described his responsibility to the university at large and his commitment to creating a climate of comprehensive excellence and success for his student-athletes."
Dykes has been at Louisiana Tech for three seasons, compiling a 22-15 record. The Bulldogs went 9-3 this season, but turned down a chance to play in the Independence Bowl and then did not receive an invitation from any other bowl game.
Louisiana Tech averaged 51.5 points per game this year.
Tedford was fired after California went 3-9 in 2012 with a 2-7 record in the Pac-12 Conference. Nevertheless, Tedford leaves the Golden Bears with more wins (82) than any other football coach in school history.