The producer of the Carry On films died at his home in Gerrards Cross, Buckinghamshire, Pinewood Studios announced.
Rogers produced all 31 movies in the series between 1958's Carry On Sergeant and 1992's Carry On Columbus, and was keen to reboot the series with the long-rumoured Carry On London.
Actor Leslie Philips said: "He was 95 but he looked as though he was going to go on until [he was] 210 - he was an amazing man.
"We did have a wonderful time in those days but we weren't paid wonderful money. People that I knew and worked with him, they all loved him in spite of all that. I can afford to say I loved Peter."
Film historian and biographer Morris Bright said: "This is a sad day for British cinema. He will be greatly missed by both showbusiness colleagues and by family and friends."