Derby will take on former boss Nigel Clough's Mansfield in two English Football League competitions next term having been drawn against them in the Papa John's Trophy and Carabao Cup.
Meanwhile they will also face Mansfield in the EFL Cup first round in August.
The 35 first-round games are scheduled for the week beginning 8 August.
Elsewhere in the EFL Cup, Stockport County travel to Harrogate Town on their return to the EFL while fellow National League promotion winners Grimsby Town welcome Crewe Alexandra.
Bolton Wanderers face off against local rivals Salford City and Sheffield Wednesday and Sunderland meet again after their League One play-offs semi-final last season, while Ipswich Town take on nearby Colchester United.