Posh sacked Mark Cooper on Monday, just two months after he had replaced Darren Ferguson as manager at London Road.
Gannon told the official club website: “It is a fantastic opportunity and I am excited.”
“At Stockport, when I went there they were seven points adrift and we stayed up, so it can be done,” the 41-year-old continued.
“Statistically, it looks a difficult task, but the main aim is to get three points on Saturday (against QPR), try and make a difference and bring back some positive football.
“I am sure the fans have been dispirited by some of the results of late, I think what everyone wants to see is players playing their football in the right way and showing their true colours.
“Once they do that, I am sure the fans will enjoy their football and it can be a more enjoyable end to the season. I have spoken to two or three of the players already and they know what I want to try and achieve.”
