Forest accelerated their pursuit of Dyche after Ange Postecoglou was immediately sacked following Forest's 3-0 defeat to Chelsea.
The former Everton and Burnley manager, who was a youth player at Forest, will take charge of the club's Europa League match against Porto on Thursday.
Signing a contract until summer 2027, Dyche becomes Forest's third manager of the season with Postecoglou succeeding Nuno Espirito Santo after the Portuguese fell out with owner Evangelos Marinakis and chief Edu Gaspar.
Former Tottenham boss Postecoglou only held the position for 39 days, though, as he was axed with no wins from eight games – the shortest permanent managerial reign in Premier League history.
Marinakis had considered other candidates, including ex-Manchester City manager Roberto Mancini and Fulham's Marco Silva, but Dyche emerged as the frontrunner.
Dyche has been out of work since January after leaving Everton following a two-year stint at Goodison Park.
He kept the Toffees in the Premier League in 2023/24 despite points deductions for breaches of the Premier League's financial rules.
Prior to that, Dyche managed Burnley for nine and a half years in a period which brought regular Premier League football to Turf Moor.