The draw was held at The Deep Aquarium in Hull, and with manager Steve Bruce watching on his side were second to be drawn out, sending them to The Emirates Stadium.
"We'd been drawn against Arsenal in the rehearsal," Bruce told BBC Sport.
"Let's hope it is as good as the final, because it was a great game."
Tigers captain Curtis Davies said: "I guess it was just meant to be."
The third round, which takes place over the first weekend of January (3 to 4), sees the Premier League and Championship clubs join the competition.
League Two AFC Wimbledon - in the third round for the first time in their 12-year history - will host Liverpool in a match which will have many reminiscing about the 1988 final, won by the original Wimbledon.
There were eight non-League sides in the hat, with the pick of the ties involving those teams seeing Dover Athletic drawn with the Premier League's Crystal Palace.
Stoke play Wrexham in another match which pits the game's elite against a side whose memorable giant-killing act was a defeat of Arsenal in 1992, while West Brom host Gateshead.
There will be four all-Premier League ties: Burnley v Tottenham, Leicester v Newcastle and Everton v West Ham, plus Arsenal v Hull.
Chelsea, the Premier League leaders and FA Cup winners in four of the last eight seasons, will host Watford of the Championship.
Louis van Gaal's Manchester United must go to either Accrington or Yeovil, who first play in a second-round replay.
Manchester City, the 2011 winners, play at home to Sheffield Wednesday.
There are six confirmed all-Championship ties, with the Lancashire derby between Bolton and 2013 winners Wigan the pick.
Chesterfield, whose place in the competition could be in jeopardy after they were charged by the FA with fielding an ineligible player in their second-round win at MK Dons, were drawn to play Scunthorpe or non-League Worcester.
Source : PA