Baylor has found its replacement for Matt Rhule.
Aranda's exit is the latest major loss for the national champions following the departures of senior quarterback Joe Burrow and wunderkind offensive assistant Joe Brady to the NFL.
The 43-year-old has been at LSU since 2016 and is the nation's highest-paid assistant at $2.5 million.
LSU has finished inside the top 25 in total defense in three of four seasons under Aranda, who previously held the same role with Wisconsin from 2013-15.
Aranda will be tasked with building on the success of Rhule, who rebuilt the Bears and led them to an 11-3 finish and a berth in the Sugar Bowl before leaving to become the Carolina Panthers' head coach. Brady will join Rhule in Carolina as his offensive coordinator.