Satterfield, 45, replaces Bobby Petrino, who was fired Nov. 11 after leading the Cardinals to a 2-8 record.
Satterfield received a six-year contract worth $3.25 million per year with a $5 million buyout.
Satterfield was in his sixth season with Appalachian State, where he was a quarterback from 1992 to '95. He compiled a 51-24 record as coach and led the high-scoring Mountaineers to a 10-2 record this season. On Saturday, they beat Louisiana 30-19 to win their third consecutive Sun Belt championship.
Louisville set its sights on Satterfield as soon as Jeff Brohm turned the Cardinals down, opting to remain at Purdue.
"When I set out looking for a new head coach, I recognized Scott early in the process as someone I was confident in leading this football program," athletic director Vince Tyra said in a statement. "Following his career very closely, his teams are statistically very sound on both sides of the football. Both his offenses and defenses are ranked high nationally, and I valued how well-prepared and well-coached his teams have always been at Appalachian State."
Satterfield expressed his thanks to Tyra and Neeli Bendapudi, Louisville's president, in the statement.
"Words cannot express how grateful I am. I have two immediate obligations: mold these young men into productive members of society and put a competitive team on the field that's going to work extremely hard to win games," Satterfield said. "I understand there are high expectations here, but as a program, we will do things the right way and develop men of high integrity and character. We will build a program that our fans will be extremely proud of on and off the field."
ESPN's David Hale contributed to this report.