"The former Forest youth player joins the club on a contract running until the summer of 2027 and will take charge of his first match on Thursday night as the Reds take on FC Porto in the Europa League," Forest said in a statement on Tuesday.
Forest sacked Postecoglou barely 20 minutes after the final whistle blew in their 3-0 home defeat to Chelsea on Saturday, a loss that left the Midlands side 18th in the league standings with five points from eight matches.
Postecoglou's Forest reign of just 39 days made him the shortest-serving permanent Premier League manager to be sacked mid-season.
"A respected and experienced Premier League manager, Dyche brings the perfect blend of character, tactical acumen and proven achievement to guide the club through its next chapter," Forest said.
"As a former Forest youth player who lives locally, Dyche also has a deep understanding of the values and pride of Forest and its supporters."
Dyche, 54, has been out of work since January when he was sacked by Everton after a poor run of results.
The Englishman's most notable managerial achievements came during his decade-long tenure at Burnley from 2012 to 2022.
During that period, he guided the Clarets to promotion twice from the Championship, secured two top-half league finishes and led the club to European qualification for the first time in 51 years.
His other managerial spell came at Watford.
Known for his pragmatic approach and defensive organisation, Dyche will be tasked with steadying the ship at Forest, who have struggled since the September sacking of Nuno Espirito Santo, now manager of West Ham United.
Forest next host Porto in the Europa League on Thursday before visiting high-flying Bournemouth in the Premier League on Sunday.
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