The 19-year-old, who has one cap for his country, joined Chelsea from Vasco da Gama in January before being loaned back in March.
He scored eight goals in 33 appearances as Vasco secured promotion to Brazil's top flight in 2022.
"I am very happy and excited to be here. I know Forest is a big club," said Santos.
"They have good players and play good football, which is important to me. It has always been my dream to play in the Premier League and I can't wait to enjoy playing."
In February, Santos captained Brazil to victory in the South American Under-20 Championship, finishing the tournament as joint top scorer with six goals.
He was rewarded with his first senior call-up in March, making his debut against Morocco.
He has yet to make a senior appearance for Chelsea but featured regularly for Mauricio Pochettino's side in pre-season.
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