Nottingham Forest will face Derby in the second round of the Carabao Cup, while Leicester will visit Newcastle.
The draw, which saw the inclusion of the 13 Premier League clubs who are not competing in European competitions, as well as Championship sides Cardiff and Fulham, was once again regionalised into North and South sections.
Forest last faced fellow Championship rivals Derby in a cup fixture in the FA Cup a decade ago when the Rams progressed over two legs.
Leicester, managed by Brendan Rodgers, were beaten by eventual champions Manchester City in the quarter-finals last season and meet Steve Bruce's Newcastle in the only all-Premier League meeting.
Elsewhere, Everton face a difficult assignment against Lincoln who have enjoyed good cup success in previous years, including their run to the FA Cup quarter-finals in 2016/17.
Newport will host two-time runners-up West Ham, while fellow League Two side Forest Green Rovers will travel to Bournemouth after respective penalty shoot-out victories against Gillingham and Charlton.
Leeds, who defeated Salford 3-0 on Tuesday, were drawn at home against Stoke as Premier League clubs Watford, Crystal Palace, Burnley and Sheffield United will all play at home against Coventry, Colchester, Sunderland and Blackburn.
Norwich will travel to face Crawley while Aston Villa, who were also promoted to the Premier League last season, will also face League Two opposition at Crewe and Southampton will face Fulham at Craven Cottage.
Second round fixtures are scheduled to take place in the week commencing August 26.
Clubs competing in Europe during the 2019-20 season will finally enter the Carabao Cup in round three.
Carabao Cup second-round draw
South section
Plymouth vs Reading
Crawley vs Norwich
Newport vs West Ham
Oxford Utd vs Millwall
Watford vs Coventry
Swansea vs Cambridge Utd
Cardiff vs Luton
Bristol Rovers vs Brighton
Crystal Palace vs Colchester
Fulham vs Southampton
Bournemouth vs Forest Green
Southend vs MK Dons
QPR vs Portsmouth
North section
Crewe vs Aston Villa
Lincoln vs Everton
Leeds vs Stoke
Sheffield Utd vs Blackburn
Rotherham vs Sheffield Wednesday or Bury
Newcastle vs Leicester
Burton vs Morecambe
Burnley vs Sunderland
Nottingham Forest vs Derby
Grimsby vs Macclesfield
Preston vs Hull
Rochdale vs Carlisle