Newly-promoted Sutton United will travel to face Championship side Cardiff City in their first-ever Carabao Cup tie.
Sheffield United, the only relegated Premier League team in the draw, will face Carlisle in the first round.
The 35 round one fixtures are scheduled to take place during the week beginning 9 August.
Elsewhere, Sheffield Wednesday take on Huddersfield in a Yorkshire derby while Forest Green play Bristol City.
Hartlepool face Crewe Alexandra on their return to league football after their National League promotion final win last weekend.
Derby County, who were fined £100,000 over some of their accounting policies earlier on Thursday, have been drawn against League Two side Salford City.