Relegated Sunderland will travel to Bury in the EFL Cup first round.
Forest Green, promoted from the National League, will host MK Dons in their first appearance in the competition, while FA Cup giant-killers Lincoln will be away to Rotherham.
The 35 ties will be played in the week commencing Monday, 7 August.
Hull City and Middlesbrough have been handed a bye into the second round, having finished above Sunderland in the Premier League last season.
Confusion over draw
There was confusion after the draw, which was streamed live from Bangkok, where the competition's new sponsors, energy-drink company Carabao, are based.