Darren Ferguson's men were runners-up to Leicester in League One last season and will start against Clough's troops as the sons of two managerial greats go head to head.
Clough told the club's official website: "Pride Park will no doubt be full to bursting on August 8 when we get under way. With it being Peterborough's first game back at this level they will no doubt sell out the away end and everyone knows how good our backing is.
"Peterborough are a fantastic side who have been together for some time and are used to winning football matches. To be honest, I think it is as tough a fixture as we could have drawn first up.
"Likewise, our second game of the campaign at Scunthorpe. We will certainly have to be ready to knuckle down from the first whistle because both these teams will have their tails up."