The 19-year-old midfielder last night decided to move to the City Ground after failing to make Mauricio Pochettino’s squad for the 3-1 defeat to West Ham on Sunday.
Santos, a £16million signing from Vasco da Gama in January, is highly regarded at Stamford Bridge but has found himself on the fringes of Pochettino's squad.
Chelsea made three major midfield signings this summer with Moises Caicedo, Romeo Lavia and Lesley Ugochukwu joining the club for a combined total of almost £200m.
The one-time Brazil international joins Steve Cooper’s side in a bid to play first-team football. The deal is unrelated to Chelsea’s interest in Forest forward Brennan Johnson.
Cooper has an outstanding track record developing young talents and Santos is looking forward to playing alongside Forest’s two Brazilians players, Danilo and Felipe.
Santos is hoping to be registered in time to make his debut against Manchester United at Old Trafford on Saturday.