Nuno - formerly of Wolves and Tottenham - replaces Cooper who was sacked on Tuesday following a poor run of form which saw 17th-placed Forest pick up just one win in 13 games.
The Portuguese has penned a two-and-a-half-year deal at the City Ground until 2026 and his first game in charge comes on Saturday when Forest host Bournemouth in the Premier League.
The job will be Nuno's first since November when he was sacked by Saudi Arabian side Al Ittihad.
Nuno spent four years at Wolves and helped them gain promotion from the Championship and leading them to consecutive seventh-place finishes while enjoying a run to the Europa League quarter-finals.
The 49-year-old departed the club in the summer of 2021 and joined Spurs, although his tenure in north London would prove to be ill-fated.
Nuno was sacked less than three months into his role following a run of five defeats in seven games.
He then joined Al Ittihad in July last year and guided the side to the Saudi Pro League title but was dismissed into the new campaign after a poor spell of form.
