Arsenal's reward for beating London rivals Tottenham on Saturday is a home tie against League One Coventry City in the fourth round of the FA Cup.
The Gunners, who were knocked out by Blackburn in the fifth round in 2013, last lifted the trophy in 2005.
Chelsea will host Stoke, while Manchester City will play Watford if they defeat Blackburn in their third-round replay.
Ties will be played on 25 and 26 January.
Swansea's reward for beating Manchester United at Old Trafford is a trip to Championship side Birmingham City.
Holders Wigan will entertain Crystal Palace after beating MK Dons in their replay after the two sides drew 3-3 in their first meeting.
Roberto Martinez's Everton head to League One Stevenage, while Ole Gunnar Solskjaer's Cardiff will travel to Championship side Bolton Wanderers.
Liverpool, who defeated League One Oldham 2-0 in their third-round fixture, will travel to Championship side Bournemouth.
Hull City travel to League Two Southend, who are managed by former Tigers boss Phil Brown.
"You couldn't write the script, it really is what the FA Cup is all about," said Brown, who managed Hull from 2006 until 2010.
"One of my ambitions when I arrived at Southend United was to fill the stadium and I think we can do that against Hull."
Kidderminster are the only non-league side left in the competition after beating League One promotion hopefuls Peterborough in their third-round replay. They will travel to Premier League strugglers Sunderland in the fourth round.
FA Cup fourth-round draw
Sunderland v Kidderminster
Bolton v Cardiff
Southampton v Yeovil
Huddersfield v Charlton or Oxford
Port Vale v Brighton
Nottingham Forest v Preston
Southend v Hull
Rochdale v Sheffield Wednesday
Arsenal v Coventry
Stevenage v Everton
Wigan v Crystal Palace
Chelsea v Stoke
Blackburn or Manchester City v Watford
Bournemouth v Liverpool
Birmingham v Swansea
Sheffield United v Fulham