Bradley comes to the Bruins after spending the 2014 season as West Virginia's senior associate head coach, where he was in charge of the defensive line. He replaces Jeff Ulbrich, who left earlier this month to become the linebackers coach for the NFL's Atlanta Falcons.
Bradley previously served as Penn State's defensive coordinator from 2000-2011 and as interim head coach for four games in 2011.
"To bring a coach of Tom Bradley's caliber to UCLA is very exciting," said Bruins coach Jim Mora. "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."
Bradley was named the Associated Press' Defensive Coordinator of the Year in 2005, when the Nittany Lions went 11-1 and won the Orange Bowl. For six straight seasons from 2004 to 2009, Penn State's defense ranked in the top 15 nationally for both scoring and total defense.
Bradley, who played defensive back at PSU in the 1970s, resigned as defensive coordinator in January 2012 after the school hired Bill O'Brien as head coach.
He then took two years off from coaching to be a color analyst for CBS Sports before taking the position at West Virginia.
UCLA went 10-3 last season and won the 2015 Alamo Bowl over Kansas State.
- Molly Geary