Newcastle will host Premier League rivals Leicester in the Carabao Cup second round, while Nottingham Forest face East Midlands neighbours Derby.
There are five League Two-Premier League ties including Newport v West Ham, Crewe v Aston Villa and Crystal Palace v Colchester.
Everton will travel to League One Lincoln, while Watford host Coventry and Burnley play Sunderland.
The ties will be played the week beginning 26 August.
Leeds, who beat Salford City 3-0, face fellow Championship side Stoke.
The draw, which is split into northern and southern sections, sees the inclusion of the 13 Premier League Clubs who are not competing in European competitions, as well as Championship sides Cardiff City and Fulham.
More to follow.
Draw in full
South section
Plymouth v Reading
Crawley v Norwich
Newport v West Ham
Oxford United v Millwall
Watford v Coventry
Swansea v Cambridge United
Cardiff v Luton
Bristol Rovers v Brighton
Crystal Palace v Colchester
Fulham v Southampton
Bournemouth v Forest Green
Southend v MK Dons
QPR v Portsmouth
North section
Crewe v Aston Villa
Lincoln v Everton
Leeds v Stoke
Sheffield United v Blackburn
Rotherham v Sheffield Wednesday or Bury
Newcastle v Leicester
Burton v Morecambe
Burnley v Sunderland
Nottingham Forest v Derby
Grimsby v Macclesfield
Preston v Hull
Rochdale v Carlisle
