Fedora compiled a 45-43 record in seven seasons at UNC.
"Sally and I love North Carolina, we love this University and we are thrilled to be back, " Mack Brown said in a school release.
The Gamecocks and Tar Heels will kick off the 2019 season in the Belk College Kickoff game on Saturday, Aug. 31, at Charlotte's Bank of America Stadium.
Brown, who went 158-48 over 16 years at Texas, coach at UNC for 10 seasons before getting the Texas job and had a record of 69-46-1 with the Heels.
Texas football could be impacted any number of ways by some of the recent coaching news happening around the Power Five conferences. He also made it to the BCS National Championship in 2009 before losing to Alabama.
His last five years were spent as an ESPN college football analyst.
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The Austin American-Statesman reported that he would be interested in assembling a staff that would include former Auburn head coach Gene Chizik as his defensive coordinator and recently fired Texas Tech head coach Kliff Kingsbury as his offensive coordinator.
He started 1-10 in each of his first two seasons, but steadily built up the program through strong recruiting, particularly with instate prospects.
Head coach Mack Brown of the Texas Longhorns arrives at Cotton Bowl as the Longhorns prepare to take on the Oklahoma Sooners on October 12, 2013 in Dallas, Texas. According to IC, he's now in the process of assembling a staff. Brown coached at North Carolina for 10 years before being hired by Texas in 1997.
He had his biggest success with the Longhorns, winning the national championship in 2005 with Vince Young as his quarterback. He is 244-122-1 in his career as a head coach and 13-7 in bowl games. He has worked for ESPN and ABC sports for the last several years since leaving Texas following the 2013 season.
Brown, of course, coached North Carolina for 10 seasons in the 1980s and 1990s.