The 58-year-old Chavis has been the defensive coordinator under Les Miles at LSU since 2009. He won the Broyles Award as the nation's top assistant coach in 2011.
This season, LSU ranked fourth nationally -- and second in the SEC behind Georgia -- in passing yards allowed, giving up only 162.3 yards per game.
Chavis will replace Mark Snyder, who was relieved of his duties after the regular season. The Aggies allowed an average of 38.3 points and 502.5 yards in their final seven games under Snyder's watch this season.
Under Snyder, the Aggies ranked 103rd nationally in yards allowed per game (449) and 111th in rushing defense (223.5 yards allowed per game).
"They've been very effective," Sumlin said earlier this season of the LSU defense. "They've been athletic, had some different people on the field, they've done a nice job. [Chavis] has done a nice job this year, too.
"John Chavis' record stands for itself defensively, and he's as good as there is in the country."