The 27-year-old, who won Olympic gold with Brazil in Tokyo, spent one season at Juventus after leaving Aston Villa for a fee of around 50 million euros ($57.94 million) on a five-year contract.
However, he made only 27 appearances for the Turin side.
"I am really happy to be here, it's a big club and I decided to come here because I can see the ambition the club has," Douglas Luiz said in a statement late on Thursday.
Having started his career with Brazil's Vasco da Gama, Douglas Luiz moved to Manchester City in 2017 but did not play for them and was loaned to Girona for two seasons before joining Villa in 2019.
Forest, who finished seventh in the Premier League last season, visit Crystal Palace on Sunday.
