Popular Nuno Espirito Santo started the campaign in the City Ground dugout and was replaced last month by Postecoglou, whose tenure lasted just 39 days as he was sacked following Saturday's 3-0 defeat to Chelsea.
Forest quickly turned to former Burnley and Everton boss Dyche, who has signed a deal until 2027 with a club he spent time at as a trainee during the Brian Clough era.
The 54-year-old begins his reign with a Europa League game at home to Porto on Thursday, with the Reds seeking to end a 10-match winless streak in all competitions.
Victory would be a welcome shot in the arm for a club whose ruthlessly-ambitious owner Marinakis is realistic about the job at hand as Dyche takes over a side in the Premier League relegation zone.
"I spoke to him and the people he thinks are important at the club about the prospect of it once the decision was made with the outgoing manager," Forest's latest boss said.
"He spoke very openly to me about the challenge. He's aware of the challenge. I don't think he thinks he's a gimme just because of last season.
"He does keep up with the stats and facts. He knows at the end of last season it was a challenging run where they didn't get as many points.
"He's aware of that and that's why they tried to add a bit more to try to keep moving forward.
"It was a good conversation, obviously, otherwise I wouldn't be here and there was a reality to it as well."
Forest's only win this season came on the opening day against Brentford and Dyche says they need to change tack, starting with going back to basics.
"The first thing is can we just stabilise the situation," he said. "I think everyone knows that. You guys have been writing about it for weeks.
"Then can you move it forward? But it still needs the basics putting back into the team, I think, because I think they just lost sight of that a little bit.
"That's the start point, but of course he wants more for Nottingham Forest. He wouldn't do all this if it wasn't for wanting more."
Dyche held court in open and entertaining fashion during a lengthy unveiling press conference that doubled up as the preview for Forest's match against Porto.
From impersonating Clough calling him "young ginger" as he spoke fondly about his trainee days to talking about changing tactics and banning players' snoods, the 54-year-old's excitement to be in the role was palpable.
"What a great experience to be back at Nottingham Forest as a manager and then a European night. That's a great occasion," said Dyche, confirming striker Chris Wood was "touch and go" for the game.
"Now, of course, it doesn't feel great if you don't get the right result!"
