The 23-year-old was expected to undergo his medical late on transfer deadline day ahead of the move from Strasbourg.
It’s understood the Premier League side paid €35million, including add-ons, for the pacy winger, who signed a five-year deal that runs through to 2030.
Forest reportedly stepped up their interest in the Frenchman following their shock 3-0 defeat to Premier League strugglers West Ham.
Bakwa scored five goals in 30 Ligue 1 appearances for the French club last season, as they secured European football for the first time in their history.