The former Fulham, Birmingham and West Brom striker, 38, is quitting football altogether to pursue business interests.
He told Vale's official website: "At this stage of my life I feel it is time for a change.
"I have enjoyed my time here and it will be the first result I look out for. I will always keep in contact with a lot of people here because it is a fantastic club.
"I know coming out of football I am not going to get another opportunity in it, but it's something I feel I have got to do."
Manager Micky Adams said: "Geoff will be missed by everyone around the club, including me, particularly as he and I are reigning head tennis champions. So I will be looking for a new partner next season."