The Argentine coach, who replaced Oscar Garcia at the helm in November 2020, had a contract until 2024.
Comunicado oficial: ??????? ??????#GraciasChacho— RC Celta (@RCCelta) November 2, 2022
Celta have lost four of their last five games in La Liga, only managing a draw in the other, against Getafe.
"Coudet and his technical team have left Celta after a fruitful era," the club wrote in a statement.
"The Argentine coach leaves after two years during which the club performed well. (When he arrived) the club was second from bottom, and that season the team finished eighth after a spectacular comeback.
"Last season, Celta finished 11th. The club, after this difficult decision, wants to offer Coudet and his assistants their most sincere gratitude for what they gave, the honesty and professionalism they showed from the first day of their time in Vigo."
The club has appointed former Sheffield Wednesday coach Carlos Carvalhal later on Wednesday, on a two-year deal, ahead of their game against Osasuna on Saturday at Balaidos.