ESPN's Joe Schad reported on Dec. 14 that Ohio State would be hiring Withers, who confirmed his move Wednesday.
"We've known each other for a couple years," Withers said of Meyer. "A few years ago we talked when the Florida defensive coordinator job came open. So we've got a little bit of a past and I'm looking forward to the future with Coach Meyer."
A few hours later, Ohio State announced it had hired Withers.
"Everett is extremely well-respected across the country," Meyer said in a statement. "I've known about him for a number of years and followed his progress as a college and NFL assistant coach. He will be a great fit for this staff and I think he and Luke (Fickell) are going to work well together as the co-coordinators of our defense."
Withers has been a college coach for 17 years and has also worked seven seasons in the NFL, including six years (2001 to 2006) as defensive backs coach with the Tennessee Titans under Jeff Fisher.
He led North Carolina to a 7-5 record this season after taking over in July for Butch Davis, who was fired amid an NCAA investigation.
Withers will coach the Tar Heels through their AdvoCare V100 Independence Bowl against Missouri on Dec. 26, and soon after head to Columbus to start his new job.
Joe Schad is an ESPN college football reporter. Information from The Associated Press was used in this report.