Non-league Barrow have been handed a trip to Middlesbrough after the draw for the FA Cup third round took place.
Histon's reward for beating Leeds is a home tie with Swansea and Eastwood Town travel to Notts County or Kettering.
The winners of the replay between Blyth and Bournemouth face Blackburn, Forest Green play Derby and fellow non-leaguers Torquay entertain Blackpool.
Cup holders Portsmouth take on Bristol City, Manchester United travel to Southampton and Arsenal host Plymouth.
Although his players looked underwhelmed when they were paired with Swansea, Histon boss Steve Fallon said it was a good chance to reach the fourth round.
"Obviously, we wanted to be at home; that's all you want," he said.
"You could have the big boys but Swansea are a big side in their own right. It's a good little tie for us and I'm sure we'll have a full house again and maybe a chance of getting to the fourth round."
Barrow booked their place in round three with victory over Brentford, Torquay overcame fellow Blue Square Premier side Oxford and Eastwood pulled off one of the shocks of the round with victory over Wycombe.
Kidderminster Harriers, the last non-league side to make the last 16 of the FA Cup, face a trip across the West Midlands to Championship side Coventry City.
FA Cup third round draw:
Portsmouth v Bristol City
Sheffield Wed v Fulham
Preston v Liverpool
Birmingham v Wolves
West Ham v Barnsley
Middlesbrough v Barrow
Hull City v Newcastle
Hartlepool v Stoke
Chelsea v Southend
Manchester City v Nottingham Forest
Cardiff v Reading
Ipswich v Chesterfield or Droylsden
Charlton v Norwich
West Brom v Peterborough or Tranmere
Torquay v Blackpool
Leyton Orient v Sheffield United
Southampton v Manchester United
Millwall v Crewe
Histon v Swansea
Forest Green Rovers v Derby
QPR v Burnley
Leicester v Crystal Palace
Tottenham v Wigan
Cheltenham v Doncaster
Arsenal v Plymouth
Notts County or Kettering v Eastwood Town
Bournemouth or Blyth Spartans v Blackburn
Macclesfield v Everton
Watford v Scunthorpe
Sunderland v Bolton
Coventry v Kidderminster
Gillingham or Stockport v Aston Villa
Ties will be played on the weekend of 3-4 January