The north London heavyweights will meet at White Hart Lane in the third round, in an unwanted early local derby for both Mauricio Pochettino and Arsene Wenger.
Both sides have been particularly underwhelming in the Premier League so far, and it remains to be seen whether either team will be able to pick up form before the high-profile derby.
Elsewhere, Midlands pair Birmingham City and Aston Villa (who ousted Notts County in extra time in round two) will meet at Villa Park.
Liverpool, who have won the competition eight times, welcome Carlisle United to Anfield, while Manchester United host Ipswich Town at Old Trafford.
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Chelsea have a fairly straightforward tie at Walsall, while Manchester City have arguably an easier ride of it, as they face Premier League strugglers Sunderland.
Draw in full:
Middlesbrough v Wolves
Norwich v West Brom
Hull v Swansea
Leicester v West Ham
Aston Villa v Birmingham
Tottenham v Arsenal
Manchester United v Ipswich
Liverpool v Carlisle
Crystal Palace v Charlton
Fulham v Stoke
Sunderland v Man City
Newcastle v Sheffield Wednesday
Reading v Barnsley or Everton
Preston v Bournemouth
Walsall v Chelsea
MK Dons v Southampton