His dismissal followed a goalless Premier League draw against Wolverhampton Wanderers on Wednesday.
Dyche is the third manager to be relieved of his duties by Forest this season.
The club currently sits 17th in the Premier League table, one place above the relegation zone with 12 matches remaining.
Several names, including Ole Gunnar Solskjaer, Roberto De Zerbi, Vitor Pereira, Enzo Maresca and Thomas Frank are being linked with the vacant managerial position.
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