The Chattanooga Times Free Press reports that most workers at the company's former headquarters in Chattanooga will be gone by April.
The accounting department and a few top executives will be the last to leave Tennessee.
Krystal will occupy the first and sixth floors of an office building in Dunwoody, just north of Atlanta.
Krystal spokeswoman Robin Derryberry says the company hopes to leave behind a legacy in downtown Chattanooga in the form of a museum and company store. She said the company has been gathering memorabilia over the past few months, including more than 7,000 photographs.