The 54-year-old became Forest's third manager this season when he was named as successor to Ange Postecoglou, who was sacked 39 days after replacing Nuno Espirito Santo.
Former Watford, Burnley and Everton manager Dyche's main focus will be arresting Forest's Premier League slide, but he starts with a Europa League tie at home to Porto on Thursday.
Addressing the media for the first time on Wednesday, Dyche said he takes a great deal of pleasure in managing the two-time European champions with whom his career began as a youth team player in the late 1980s.
"I have a longer history with the club from 87 to 90 and remember walking down the river (Trent) and Del Boy (Brian Clough's dog) running past you and the voice of Brian Clough in earshot," Dyche told reporters.
"All the legends that played at that time, and there were some top players, and you know, you're thinking I just want to pull that shirt on, and now to round the circle and be here as manager is something quite big for me. But I'm not just here for a fun time, there's a job to be done."
Dyche, who parted ways with Everton in January after two years at the helm, will be assisted by former Forest players Ian Woan, Steve Stone, Tony Loughlan and Billy Mercer.
"They've got a deeper history than me here, but obviously it's fast forward now, it's a considerably different club."
Under the pragmatic Espirito Santo, Forest finished seventh last season in the Premier League after challenging for the Champions League places. Postecoglou's more expansive approach failed dismally, so Dyche, known for his direct style of play, was asked what Forest fans can expect from him.
"We've got to get back to winning ways," Dyche, whose only previous experience of managing a club in a European tie was a Europa League playoff in 2018 with Burnley, said.
"They weren't winning at the end of last season after they perhaps ran out of steam and it's not been a great start this season. But this is a good group, a very talented group and they showed that willingness and desire last season to the world.
"Now we have to reignite that."
On the current fashion for set pieces and long throws, Dyche said there were many ways to win a game.
"I did a podcast with (former Stoke City manager) Tony Pulis and Tony is now being lauded for long throws, but before he was getting hammered for long throws. It's the fashion of football, it changes all the time. I'm not pontificating one way or the other, the bit I like is when you win."
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