Holders Chelsea will have a testing game at Everton after hammering seven past Ipswich, while Fulham will host Tottenham in an all-Premier League tie.
Manchester United face a trip to League One Southampton in the fourth round of the FA Cup in a repeat of the 1976 FA Cup Final.
The winner of the third-round replay between Arsenal and Leeds will entertain Huddersfield Town.
Stevenage knocked out Newcastle in a third round upset and have been drawn at home to Reading, who beat West Brom.
League Two Burton Albion stunned Middlesbrough to make it into the last 32 and face another Championship side in Burnley in the next round, with the game taking place at Turf Moor.
League One Notts County won at top-flight Sunderland to secure their progress and will be at home in the fourth round against either Leicester or Manchester City who drew 2-2.
Full FA Cup fourth round draw :Torquay v Crawley Town or Derby
Watford v Brighton
Bolton v Wigan
Arsenal or Leeds v Huddersfield
Fulham v Tottenham
Everton v Chelsea
Southampton v Manchester United
Swansea v Leyton Orient
Burnley v Burton
Birmingham v Coventry
Doncaster Rovers or Wolves v Stoke or Cardiff
Notts County v Leicester or Man City
Stevenage v Reading
Aston Villa v Blackburn Rovers
West Ham v Nottingham Forest
Sheffield Wednesday v Wycombe or Hereford
Ties to be played over the weekend of 29 and 30 January