FA Cup holders Arsenal will begin the defence of their trophy against Hull City, in a repeat of last season's final.
The Gunners won their first piece of silverware in nine years when they came from behind to claim a 3-2 win against the Tigers at Wembley in May.
Meanwhile, Conference Premier side Dover Athletic, who shocked Cheltenham Town in the last round, will host Crystal Palace.
Manchester City have been drawn at home to Sheffield Wednesday, while Premier League leaders Chelsea welcome Watford.
The winners of Accrington Stanley and Yeovil Town's second-round replay will play host to Manchester United and Liverpool have been handed an away tie against League Two outfit AFC Wimbledon.
Elsewhere, Everton face West Ham United, Leicester City take on Newcastle United and Burnley go head to head with Tottenham Hotspur, in the three all-Premier League ties.
FA Cup third-round draw in full:
Arsenal vs. Hull City
Southampton vs. Ipswich Town
Stoke City vs. Wrexham
Charlton Athletic vs. Blackburn Rovers
Dover Athletic vs. Crystal Palace
AFC Wimbledon vs. Liverpool
Manchester City vs/ Sheffield Wednesday
Aldershot/Rochdale vs. Nottingham Forest
West Bromwich Albion vs. Gateshead
Blythe Spartans vs. Birmingham City
Aston Villa vs. Blackpool
Rotherham vs. AFC Bournemouth
Huddersfield Town vs. Reading
Oxford United/Tranmere Rovers vs. Swansea City
Cardiff City vs. Colchester United
Bolton Wanderers vs. Wigan Athletic
Sunderland vs. Leeds United
Burnley vs. Tottenham Hotspur
Millwall vs. Bradford City
Derby County vs. Southport
Brentford vs. Brighton & Hove Albion
Fulham vs. Wolverhampton Wanderers
Leicester City vs. Newcastle United
Scunthorpe/Worcester City vs. Chesterfield
Everton vs. West Ham United
Cambridge United/Mansfield Town vs Bury/Luton Town
Chelsea vs. Watford
Barnsley/Chester vs. Middlesbrough
Queens Park Rangers vs. Sheffield United
Accrington Stanley/Yeovil Town vs. Manchester United
Preston North End vs. Norwich City
Doncaster Rovers vs. Bristol City
Ties to be played between January 3 and January 6.
