The Premier League team will pay €35 million, including additional payments, for the pacy winger. He is set to sign a five-year contract that will run until 2030.
The interest in Bakwa from Forest increased after their surprise 3-0 defeat to West Ham in the Premier League.
Bakwa scored five goals in 30 Ligue 1 appearances for Strasbourg last season, helping the team secure a spot in European football for the first time in their history.