Cup holders Wigan Athletic were given a home draw with Milton Keynes Dons while last year's beaten finalists Manchester City will go to Blackburn Rovers.
Of the non-league sides, Macclesfield were drawn at home to Sheffield Wednesday, Grimsby will take on Huddersfield Town at Blundell Park and Kidderminster have a home tie against Peterborough.
Manchester United face Swansea City at Old Trafford while Chelsea will travel to Derby County.
Liverpool will face a home tie against either Mansfield, who they beat in the third round last season, or Oldham Athletic, who knocked them out in the fourth.
But the stand out tie is the north London derby and both sides will be hoping to go all the way. Arsenal boss Arsene Wenger concedes his side could have been handed an easier first hurdle.
"There are not enough tough games, they gave us another one," he quipped when asked about the draw following Arsenal's 1-1 league tie with Everton, a result that left the Gunners five points clear at the top of the standings.
Jose Mourinho's Chelsea have also not been handed a straightforward third-round tie as they must go to a Derby side who have moved up to fourth in the Sky Bet Championship after winning their past five matches.
Derby manager Steve McClaren said on his club's website: "It's a great draw for the club for a number of reasons. It's at home, we're up against a big opponent and that will mean a big test for the players.
"They will want to test themselves against one of the best teams in the country and Europe so I think it's great for them.
"It's exciting for the fans too and I'm sure a great crowd will be at the iPro Stadium for it as well as it should be a cracking FA Cup tie."
Barnsley v Hartlepool or Coventry
Yeovil v Leyton Orient
Liverpool v Oldham or Mansfield
Nottingham Forest v West Ham
Bristol City v Watford
Southend v Millwall
Middlesbrough v Hull
West Brom v Crystal Palace
Kidderminster v Peterborough
Doncaster v Stevenage
Stoke v Leicester
Southampton v Burnley
Newcastle v Cardiff
Rochdale v Leeds
Wigan v MK Dons
Charlton v Wrexham or Oxford
Manchester United v Swansea
Port Vale v Plymouth
Norwich v Fulham
Aston Villa v Sheffield United
Macclesfield v Sheffield Wednesday
Sunderland v Carlisle
Bolton v Blackpool
Blackburn v Manchester City
Everton v QPR
Brighton v Reading
Arsenal v Tottenham
Birmingham v Bristol Rovers or Crawley
Grimsby v Huddersfield
Ipswich v Preston
Derby v Chelsea
Bournemouth v Fleetwood or Burton
Ties to be played on the weekend of January 4/5, 2014