Reports state said Forest would pay an initial £25 million for the playmaker, with add-ons that could bring the fee to £42.5 million. Gibbs-White has represented England from Under-16 to Under-21 levels, and will wear the number 10 shirt for the club.
Gibbs-White starred for Sheffield United last season on loan from Wolves, being named as the Blades' player of the season after scoring 11 goals and registering 9 assists in the Championship.
Forest has been busy during the summer transfer window ahead of the September 1st deadline, bringing in 15 players including Jesse Lingard after his departure from Manchester United and Neco Williams from Liverpool.
Steve Cooper's side lost 2-0 at Newcastle United in their Premier League opener before beating West Ham United 1-0 last weekend. They visit Everton on Saturday.