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.
"Dyche brings the perfect blend of character, tactical acumen and proven achievement to guide the club through its next chapter," Forest said in a statement.
"Having managed more than 330 Premier League matches in his career to date, Dyche has built teams defined by defensive organisation, resilience, and strength from set pieces – qualities that align closely with the current squad's attributes and the club's footballing identity.
"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.
"With his character, tactical acumen and man-management skills, his appointment represents the best opportunity for a successful and competitive season across both domestic and European competitions."
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.