Satterfield, 39, played quarterback at Appalachian State and was an assistant coach at the school for 12 seasons. Satterfield played for Moore, who coached the Mountaineers for 24 seasons.
School officials said this month that Moore's contract wouldn't be renewed and Satterfield was installed as interim head coach.
"It is with great pride that we announce that Coach Satterfield has agreed to lead Appalachian State's football program into a new era," Appalachian State Athletic Director Charlie Cobb said.
"Scott has been successful in every role that he has filled during his 15-year coaching career and obviously has great familiarity and love for Appalachian State."
Appalachian State was 8-4 this season and won at least a share of the Southern Conference title in seven of the last eight years. It was after a second-round playoff loss this month that Moore was told he wouldn't be asked to return.
Moore, 73, built a 215-87 record at Appalachian State. He previously coached at North Texas and Texas Tech.
Satterfield was an all-Southern Conference selection as a senior when the Moore-led Mountaineers went 12-1. He played from 1992-95. He was an Appalachian State assistant from 1998-2008 and left for stints at Toledo and Florida International before return to Appalachian State before the 2012 season.