The club, placed 17th in the Premier League table, sacked Steve Cooper after a run of one win in 13 matches.
Nuno was relieved of his duties at Saudi Arabia's Al-Ittihad last month.
He spent a short amount of time with Spurs in 2021, following a successful four-year stint at Wolves.
Forest's next fixture is against Bournemouth in three days' time.
Cooper 'will remain a friend'
Forest owner Evangelos Marinakis lauded Cooper, who he said will remain "forever welcome" at the club.
"His achievement in guiding Forest back to the Premier League will undoubtedly remain an iconic moment in the club’s history," he said.
“We thank Steve for his dedication and commitment during his time with us, as well as the incredible connection he forged with our supporters and the city of Nottingham.
“Steve will always remain a friend of the club and will forever be welcome at the City Ground."
