Dyche was relieved of his duties following a goalless Premier League draw with bottom-side Wolves on Wednesday night, having been in charge at the City Ground for just 114 days.
Forest's failure to convert any of their numerous chances against Wolves left them three points clear of the relegation zone.
A club statement said: "Nottingham Forest Football Club can confirm that Sean Dyche has been relieved of his duties as head coach.
"We would like to thank Sean and his staff for their efforts during their time at the club and we wish them the best of luck for the future.
"We will be making no further comment at this time."
Forest finished seventh in the Premier League under Nuno Espirito Santo last season, missing out on a Champions League spot after a poor end to the campaign but securing European football for the first time since 1995-96.
Nuno signed a new three-year deal at the City Ground in June 2025, but was sacked in September after a breakdown in his relationship with owner Evangelos Marinakis.
Ex-Tottenham boss Postecoglou was swiftly brought in as the Portuguese's replacement, but lasted only 40 days in the job with Marinakis wielding the axe again within minutes of a 3-0 defeat to Chelsea.
Dyche, who lives in Nottingham and was a trainee at the club, became the club's third first-team boss of the season on October 21 and was joined in the dugout by former Forest heroes Ian Woan and Steve Stone.
They beat Porto in his first game in charge and looked to have turned a corner after a 3-0 win at Premier League champions Liverpool a month later.
Wednesday's draw left Forest with just two wins from their last 10 in the Premier League - a run during which they also exited the FA Cup to Championship Wrexham - as they struggled to pull away from trouble in the fight for survival.
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