Roof left his alma mater last month in what appeared to be a mutual decision, becoming the co-defensive coordinator and associate head coach at NC State.
Woody is a 27-year coaching veteran who directed Appalachian State's defense the past five seasons. After putting in an attacking 3-4 scheme, the Mountaineers led the Sun Belt Conference in total defense three times and ranked among the top 30 nationally each of the past four seasons.
Appalachian State closed out this season with a 34-0 rout of Toledo in the Dollar General Bowl.
Woody becomes the fifth defensive coordinator in Paul Johnson's decadelong tenure as coach. Roof served in the role longer than his predecessors -- five seasons -- but Johnson was clearly frustrated after the defense failed to protect late leads against Tennessee and Miami.
Roof's departure was essentially sealed in the season finale, a 38-7 loss to rival Georgia that capped a 5-6 season. The Yellow Jackets missed out on a bowl for the second time in three years.
Prior to coaching at Appalachian State, Woody spent a total of 22 years over two stints at his alma mater, Wofford. He was defensive coordinator from 2000 to 2012.
"He's achieved a lot of success and helped his teams win a lot of games at Appalachian State and Wofford," Johnson said in a statement. "I think he's a great fit for our program."