Elsewhere, defending champions Manchester City are at home to Huddersfield Town, Chelsea host Preston North End, Spurs will play Burnley and Manchester United travel to Wigan.
Non-league Maidstone will have a home draw against either Stevenage or Port Vale, while National League side Eastleigh will play Barnet or Newport should they get past Reading on Sunday.
Ramsgate will face Championship side Ipswich should they beat AFC Wimbledon on Monday.
Other all-Premier League ties include Crystal Palace against Everton and Brentford versus Wolves.
FA Cup third round draw in full
Luton Town v Bolton Wanderers
Shrewsbury Town v Wrexham OR Yeovil Town
Stoke City v Brighton and Hove Albion
Norwich City v Crewe Alexandra OR Bristol Rovers
West Ham United v Bristol City
Tottenham Hotspur v Burnley
Fulham v Rotherham United
West Bromwich Albion v Aldershot OR Stockport County
Southampton v Alfreton Town OR Walsall
AFC Wimbledon OR Ramsgate v Ipswich Town
Peterborough United v Leeds United
Millwall v Leicester City
Watford v Chesterfield OR Leyton Orient
Sunderland v Newcastle
Sheffield Wednesday v Cardiff City
Crystal Palace v Everton
Middlesbrough v Aston Villa
Nottingham Forest v Blackpool OR Forest Green Rovers
Wigan Athletic v Manchester United
Manchester City v Huddersfield Town
Blackburn Rovers v Cambridge United
Gillingham v Sheffield United
Swansea City v Morecambe
Chelsea v Preston North End
Queens Park Rangers v Bournemouth
Coventry City v Oxford United
Brentford v Wolverhampton Wanderers
Plymouth Argyle v Sutton United
Maidstone United v Stevenage OR Port Vale
Newport OR Barnet v Eastleigh OR Reading
Hull City v Birmingham City
The third round is scheduled to take place on the weekend of Saturday, January 6th.
