The Anzhi Makhachkala midfielder, who is viewed as a direct replacement for wantaway Gareth Bale, is expected to undergo a medical in London on Wednesday.
Willian had been linked with a move to Liverpool but appears to have been lured by the guarantee of European football at White Hart Lane this season.
The deal, which could be done before Sunday's home clash with Swansea, would be the third time Spurs have broken their transfer record this summer, following the £17million and £26million arrivals of Paulinho and Roberto Soldado respectively.
Spurs could yet add Roma striker Erik Lamela to their ranks in a double deal that would take their outlay during this window to almost £120million.
Bale, meanwhile, is still to secure a proposed world-record move to Real Madrid but it is understood a resolution to the saga of the summer could now come within days.