Marco Zaffaroni quit Verona on Tuesday after guiding the team to Serie A safety via a relegation play-off this month.
In a statement, Verona said that Zaffaroni had told the club that he "no longer wished to continue his time in the Gialloblu dugout."
Zaffaroni took over Verona in early December with the team bottom of Italy's top flight with just five points from their first 15 matches.
Verona finished 18th, just inside the drop zone, but were saved from direct relegation by ending the season level on 31 points with 17th-placed Spezia.
They then beat Spezia 3-1 in the play-off a fortnight ago to stay in the division and relegate their opponents.
