FA Cup holders Arsenal will begin the defence of their trophy at home to Sunderland in the third round.
Premier League Liverpool face a trip to League Two Exeter, while the top flight's bottom club Aston Villa also go to a League Two side in Wycombe.
There are five all-Premier League ties, with Spurs hosting leaders Leicester.
Non-league Eastleigh are at home to Bolton, while Everton will host League Two side Dagenham & Redbridge, who beat non-league Whitehawk in a replay.
The non-league hopefuls
Eastleigh are currently eighth in the National League and face a Bolton side struggling at the foot of the Championship.
"We will be looking forward to that tie," said Eastleigh boss Chris Todd.
All-Premier League ties
Arsenal have won the FA Cup a record 12 times and will be aiming for a third straight victory after they beat Hull in the 2014 final and Aston Villa in 2015.
Leicester are leading the way in the Premier League but the four-time FA Cup finalists have never won the competition. They face a Tottenham side aiming for a first FA Cup victory since 1991.
Manchester City claimed the last of their FA Cup victories in 2011 and, having been knocked out by Championship sides in the past two years, face struggling top-flight rivals Norwich City.
City have suffered from inconsistency this season, while the Canaries - 16th in the top flight - have won just once in their last 10 games and may welcome the distraction of the FA Cup.
Southampton won the FA Cup in 1976 but have have not gone further than the fifth round in the past 10 seasons, and they will welcome former manager Alan Pardew's Crystal Palace, runners-up in 1990, to St Mary's Stadium for the third round.
Watford, losing finalists in 1984, host six-time winners Newcastle, who have lost in the third round in each of the past three seasons.
Aston Villa are struggling at the bottom of the Premier League and have won just twice this season so League Two promotion hopefuls Wycombe hope to cause an upset.
Both clubs have been managed by current Blackburn boss Paul Lambert - Wycombe from 2006-2008 and Villa from 2012-2015.
Swansea City face League Two leaders Oxford, who have not won a third round tie for 17 years.
Manchester United, who have won the FA Cup 11 times and host League One side Sheffield United, who were beaten semi-finalists in 2013.
The Blades have played the Red Devils four times in the FA Cup and won once, with that victory coming in 1993.
Chelsea have struggled this season in defence of their Premier League crown and have bad memories of the FA Cup from last season, when they were beaten 4-2 by League One Bradford at Stamford Bridge in the fourth round.
However, the Blues have won 17 consecutive third-round ties and will be at home against League One Scunthorpe.
FA Cup third-round draw:
Arsenal v Sunderland
Birmingham v Bournemouth
Brentford v Walsall
Bury v Bradford City
Cardiff City v Shrewsbury
Carlisle v Yeovil
Chelsea v Scunthorpe
Colchester v Charlton
Doncaster v Stoke City
Eastleigh v Bolton
Everton v Dagenham & Redbridge
Exeter City v Liverpool
Hartlepool v Derby
Huddersfield v Reading
Hull City v Brighton
Ipswich v Portsmouth
Leeds United v Rotherham
Manchester United v Sheffield United
Middlesbrough v Burnley
Newport County v Blackburn
Northampton v MK Dons
Norwich v Manchester City
Nottingham Forest v QPR
Oxford United v Swansea
Peterborough v Preston NE
Sheffield Wednesday v Fulham
Southampton v Crystal Palace
Tottenham v Leicester
Watford v Newcastle
West Bromwich v Bristol City
West Ham v Wolves
Wycombe v Aston Villa
Ties to be played 8-11 January