A busy summer at the City Ground saw Forest sign 16 players, including the 22-year-old.
Most of the summer has been spent by Forest attempting to sign Gibbs-White, who graduated from the Wolves school.
For Bruno Lage’s team this year, the Stafford-born player has started both two Premier League games.
Wolves, though, are still working to restructure Lage’s team. Thus it seemed expected that Forest would redouble its efforts to recruit him.
Forest will pay a £25 million initial cost and possible add-ons worth up to £17 million.
Gibbs-White, who has 10 England Under-21 appearances, excelled while on loan at Sheffield United last season in the Championship.
Later on Thursday, he is scheduled to have his checkup.