Cunha, a 20-year-old centre-back, made a strong impression during the Club World Cup before Botafogo's exit from the tournament.
He has now signed a five-year contract with the club, which will keep him at the City Ground until at least the summer of 2030.
Forest is set to face a challenging period as the club is expected to lose players Anthony Elanga and Morgan Gibbs-White to other teams.
Cunha's arrival is a welcome addition, standing at 6ft 6in and bringing a boost to the team's defensive line.
Forest's Chief Football Officer, Ross Wilson, expressed his excitement about the new signing.
"Jair has shown great potential in Brazil, and we are happy to have him on board," Wilson said.
"He has big ambitions and is eager to start his Premier League journey with Nottingham Forest," Wilson added.
The club's official social media account welcomed Cunha to the team, and fellow defender Murillo expressed his excitement about the new addition.