A news conference to introduce Fedora is expected to be held Friday at 1 p.m. ET, the school said.
"It's a situation I'm extremely excited about," Fedora said. "The University of North Carolina has a national brand and I think they're hungry to win championships."
North Carolina AD Bubba Cunningham, in a prepared statement, said Fedora has a strong record as a head coach and in 18 years as an assistant.
"Throughout his career his teams have been known for their exciting and highly productive offenses and aggressive defenses," Cunningham said. "Coach Fedora has a plan and a vision for the future of Carolina football that I strongly believe will make us successful on and off the field."
Fedora led Southern Miss to an upset of previously undefeated Houston in the Conference USA championship game. The Golden Eagles finished the season 11-2 and will play Nevada in the Sheraton Hawaii Bowl on Dec. 24.
Less than a week after Southern Miss won its first Conference USA title since 2003, the program is looking for a new football coach.
Fedora met with Southern Miss players and coaches on Thursday where he revealed he was leaving for North Carolina, but will coach the 22nd-ranked Golden Eagles in the bowl game.
"We want to see this thing through," Fedora said. "We want to finish this thing. This could be only team in 100 years of football that wins 12 games. We want to get that 12th win."
Southern Miss offensive lineman Joe Duhon said players were disappointed by Fedora's decision, but there were no hard feelings.
"Southern Miss is Southern Miss -- we're going to continue to win with or without" Fedora, Duhon said. "I understand his decision and still really respect him as a coach and mentor."
Fedora said Southern Miss made a "huge push" financially during the negotiations with North Carolina, "but there was more to it than just that." Fedora made a salary of $704,500 last season according to USA Today.
Fedora's departure is part of a major shakeup within the Southern Miss athletic department. Athletic director Richard Giannini announced his retirement on Thursday after 13 years in charge of the Golden Eagles.
Giannini will stay on the job through early January while Southern Miss searches for a new football coach.
The 69-year-old Giannini said in a statement that the recent success and Fedora's departure made this "a perfect time for me to retire." Giannini has overseen $68 million worth of new athletic facilities and the Golden Eagles have gone to 10 straight bowl games during his tenure.
North Carolina (7-5) plays Missouri in the AdvoCare V100 Independence Bowl two days later.
Fedora was 33-19 at Southern Miss, his first head coaching job after assistant coaching positions at Florida and Oklahoma State.
The Tar Heels were looking for a permanent coach to replace Butch Davis, who was fired shortly before training camp amid an NCAA investigation into improper benefits and academic misconduct within the program. The school then promoted defensive coordinator Everett Withers to interim coach.
Withers led the team to a 5-1 start, though the Tar Heels stumbled down the stretch by losing four of six.
Information from The Associated Press was used in this report.