The 42-year-old replaced Domenico Di Carlo at the Stadio Marc'Antonio Bentegodi in October after the Flying Donkeys lost five of their first six Serie A games.
Corini quickly stabilised Chievo, who eventually finished 12th in the league with a haul of 45 points, but the former midfielder will not build on his achievements in Verona.
A statement published on chievoverona.it read: "After reaching the set goal of booking the club a 12th season in Serie A, Chievo and coach Eugenio Corini have mutually agreed not to renew their working relationship for the 2013-14 season.
"President (Luca) Campedelli and everybody at the club thank Corini and his staff for their commitment, professionalism and constant dedication and wish them all the best for a successful future in football."
Corini, who represented Palermo for four seasons as a player, has been heavily linked with the top job at the Stadio Renzo Barbera.
The Sicilians are expected to replace coach Giuseppe Sannino in the wake of their relegation to Serie B.