De Zerbi, 37, previously managed Foggia but left the third-division side in August after two seasons with the club.
Club president Maurizio Zamparini made eight coaching changes last season.
Ballardini was initially sacked as Palermo manager in January 2016 before being reappointed in April as he helped Palermo avoid relegation.
Palermo are 15th in Serie A with one point from two games - above Inter Milan.
Zamparini, who bought Palermo in 2002, has made almost 60 coaching changes in 29 years as club owner.
Palermo have appointed Roberto de Zerbi as their new coach after Davide Ballardini resigned just two games into the new Serie A season.