Barrow are away to Derby in their first game in the competition since the 1971/1972 season, while Newport will host Swansea.
Harrogate will make their debut at Prenton Park, where they will take on Tranmere.
Championship play-off runners-up Brentford host Wycombe, who won the League One play-offs last season.
Stoke welcome Blackpool, Sunderland clash with Hull, Barnsley will host Nottingham Forest in an all-Championship affair and Charlton travel to Swindon.
All Premier League sides not involved in European competition in 2020/2021 – every team except Liverpool, Manchester City, Manchester United, Chelsea, Leicester, Tottenham and Arsenal – will enter in round two.
The first round of the Carabao Cup is due to be played on Saturday, September 5.
Round One draw, Northern section
Tranmere vs Harrogate
Crewe vs Lincoln
Walsall vs Sheffield Wednesday
Rochdale vs Huddersfield
Preston vs Mansfield
Bolton vs Bradford
Blackburn vs Doncaster
Stoke vs Blackpool
Fleetwood vs Wigan
Grimsby vs Morecambe
Middlesbrough vs Shrewsbury
Derby vs Barrow
Scunthorpe vs Port Vale
Sunderland vs Hull
Burton vs Accrington
Salford vs Rotherham
Barnsley vs Nottingham Forest
Oldham vs Carlisle
Round One draw, Southern section
Bristol City vs Exeter
Plymouth vs QPR
Swindon vs Charlton
Forest Green vs Leyton Orient
MK Dons vs Coventry
Crawley vs Millwall
Stevenage vs Portsmouth
Peterborough vs Cheltenham
Brentford vs Wycombe
Northampton vs Cardiff
Luton vs Norwich
Birmingham vs Cambridge
Newport vs Swansea
Oxford vs AFC Wimbledon
Reading vs Colchester
Gillingham vs Southend
Ipswich vs Bristol Rovers.