Andreazzoli was replaced by Iachini in early November despite leading the Tuscan team to promotion last season.
The 65-year-old beat Cagliari in the opening game of the season but then failed to register a win in the following 10 games before being sacked after a 5-1 defeat at Napoli.
His first game back in charge of Empoli, who are just a point above the relegation zone, will be against relegation rivals Frosinone on Sunday.