Of Yorkshire's six representatives in the draw, the Tigers were the only team drawn at home. The rest will be heading south in the final weekend of January.
A Tom Eaves hat-trick edged Hull past League One Rotherham United in round three, and their reward is to face one of the powerhouses of the competition in the 21st Century.
Frank Lampard's side have won the competition six times since 2000, and been runners-up twice. It would be a surprise if the game were not moved for television.
Sheffield Wednesday, who knocked Brighton and Hove Albion in round three, face Championship rivals Queens Park Rangers, while Sheffield United will also travel to the capital, to face Millwall.
Barnsley are at Portsmouth, who knocked Harrogate Town out in the first round.
Leeds United and Middlesbrough will both head to the south coast if they can reach round four.
Winning their replay at Tottenham Hotspur will see Boro face Premier League Southampton, while the winners of Monday's game between Arsenal and Leeds are at Bournemouth.