The tie between Mauricio Pochettino and Slaven Bilic’s bitter rivals is the pick of the ties for the last 16, which sees Chelsea face Everton at Stamford Bridge.
They are two of just three all-Premier League ties, completed by Manchester United’s trip to Swansea.
Elsewhere Arsenal host Championship outfit Norwich and Wolves will take on Manchester City at the Etihad Stadium.
Roy Hodgson’s Crystal Palace go away to Bristol City while Championship-toppers Leeds face Leicester at the King Power Stadium.
The final clash picked out of the pot sees Bournemouth host Middlesbrough.
Dates and times of the fixtures are to be finalised at a later date but will take place on October 23/24.
Spurs and West Ham booked their spots in the fourth round draw on Tuesday night after home wins over Barnsley and Bolton respectively.
Chelsea thrashed Nottingham Forest at Stamford Bridge 5-1, with Everton returning to winning ways thanks to a 3-0 rout of Sunderland.
Manchester United hit four once again as they strolled past Burton Albion at Old Trafford, while Swansea won 2-0 away at Reading.
FOURTH ROUND DRAW
Tottenham v West Ham
Bristol City v Crystal Palace
Swansea v Manchester United
Arsenal v Norwich
Chelsea v Everton
Manchester City v Wolves
Leicester v Leeds
Bournemouth v Middlesbrough
Fixtures to be played October 23/24