Carlo Ancelotti's side recorded an emphatic 7-0 victory over Ipswich to set up the all top-flight tie with David Moyes' improving team.
Manchester United's reward for beating Liverpool on Sunday is an FA Cup fourth-round clash at League One side Southampton.
The Saints, who beat Premier League side Blackpool 2-0 on Saturday, will face Sir Alex Ferguson's men at St Mary's on the weekend of January 29/30.
There could be as many as five all top-flight ties, with Bolton drawn at home to Wigan, Fulham up against Spurs, winners over Charlton, and Aston Villa taking on Blackburn. The winners of the replays between Doncaster and Wolves and Stoke and Cardiff will also meet.
League Two side Stevenage, who caused the shock of the round by beating Newcastle 3-1, will welcome Reading to the Lamex Stadium, while Birmingham take on Coventry in a midlands derby.
Leeds and Arsenal will replay next week with a home tie against League One promotion hopefuls Huddersfield awaiting the winner, while West Ham will be at home to Nottingham Forest and Watford play Brighton.
If Manchester City beat Leicester on Sunday they will head to Notts County, while Swansea will play Leyton Orient and Burton Albion will travel to Burnley.
The winner of Monday's game between Crawley and Derby will head to Torquay, while Sheffield Wednesday will be at home to the winner of the replay between Wycombe and Hereford.
FA Cup fourth round draw:
Torquay v Crawley 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 or Wolves v Stoke or Cardiff, Notts County v Leicester or Manchester City, Stevenage v Reading, Aston Villa v Blackburn, West Ham v Nottingham Forest, Sheffield Wednesday v Wycombe or Hereford
Matches to be played weekend of January 29 and 30.
Source: PA
Source: PA