The school made Bradley's hiring official on Tuesday.
He replaces Jeff Ulbrich, who spent three seasons with the Bruins and was promoted to defensive coordinator last season before joining Dan Quinn's staff with the Atlanta Falcons earlier this month.
Bradley spent 32 seasons with Penn State -- including 12 as defensive coordinator. He succeeded Joe Paterno as interim head coach in the wake of the Jerry Sandusky sexual abuse scandal. Many believed that, had Penn State stayed in-house, Bradley would have been Paterno's permanent successor. But he left the program following the hiring of Bill O'Brien.
Bradley spent two years working in the Pittsburgh media before joining West Virginia for one season, where he also served as assistant head coach.
"To bring a coach of Tom Bradley's caliber to UCLA is very exciting," Mora said in a statement. "His knowledge of the game, extensive experience, level of intensity and attention to detail all make him one of the best defensive teachers in college football. Combine that with the fact that he has strong national recruiting ties and is one of the most well respected coaches in the game -- it all adds up to Tom being a tremendous addition to our staff."
Bradley takes over a unit that was seventh in the Pac-12 in scoring defense (28.1 PPG) and third in total defense.