Bennett has joined Posh from Grimsby Town and has signed a four-and-a-half-year contract at London Road for an undisclosed fee.
Geohaghon and Griffiths have both signed three-and-a-half-year deals from Kettering and Dagenham respectively, their fee's are also undisclosed..
"All three have settled into life at Peterborough United very well and we are pleased they are all done and dusted," Posh mananger Mark Cooper has told Peterborough's official website.