Gibbs, a native of Beaumont, Texas, will coach linebackers for the Cowboys.
"First of all, I want to thank Coach Saban for the opportunity he gave me to be a part of his staff and to coach at LSU," Gibbs said. "Coach Saban is committed to excellence and he's certainly building something very special here at LSU. I feel very privileged to have coached at LSU and I'm very proud to have been a part of the SEC Championship as well as the Sugar Bowl win over Illinois.
"I will certainly miss the players, who have been great to work with, all of the coaches and the great LSU fans who make this a special place. The opportunity in Dallas is one in which I didn't feel I could pass up. I will certainly take a lot of great memories of LSU with me.
Some of the highlights of LSU's defense last year include a shutout against Mississippi State on the road in Starkville and limiting second-ranked Tennessee to only 20 points and 50 yards rushing in the Southeastern Conference Championship game.
"To get the opportunity to coach in the NFL with the Dallas Cowboys is great for Gary and his family," Saban said. "He did an outstanding job during his stay at LSU and we wish him a great deal of success with the Cowboys."
Saban will be hiring a new defensive coordinator for the fourth time since taking over as head coach at LSU in December 1999. His first hire, John Thompson, left after just a month on the job and took a similar post with Arkansas. Thompson is now on the new Ron Zook staff at Florida.
Phil Elmassian was hired to replace Thompson and coached one season at LSU before leaving for the coordinator's job at West Virginia. He resigned from that post after the 2001 season.
Counting position coaches, Saban has had to replace seven assistants since coming to LSU, and all but one moved on to take new coaching jobs. Defensive line Pete Jenkins announced his retirement earlier this month after 34 years of college coaching.
Gibbs came to LSU after a coaching one season with the Jim Donnan staff at Georgia. He was previously the defensive coordinator and head coach at Oklahoma, where he played for three years. Gibbs was part of Sooner national championship teams as a player and an assistant coach.