Posh look certain to drop to League One this summer, with their 4-0 defeat to Scunthorpe on Tuesday night only hastening their relegation.
"I am not driven buy personal or financial gain or a mechanical professional drive,” Gannon said on Wednesday, having hinted the night before that he would decline the opportunity to stay.
“I have become a devoted family man over the last few years and the separation from my family over the last season has created a big void in my personal happiness and contentment.
"Given that my partner is now pregnant and expecting our second baby in July, the need for their stability, security and happiness becomes increasingly important to me."
Gannon will remain in charge until the end of the season.