Aina came up through Chelsea's academy before signing for Torino on a permanent transfer in 2019. He previously played in the Premier League during a loan spell with Fulham in the 2020/21 season.
"It's exciting to be back playing in the Premier League. It's the best league in the world and I always want to challenge myself," Aina said in a statement.
Aina has been capped 30 times by Nigeria, having made his debut in 2017.
He played for England at youth level.
Forest, who finished 16th in the Premier League last season, begin their league campaign against Arsenal on August 12th.