The experienced duo, with over 950 professional appearances between them, have both signed one-year deals at Vale Park.
Manager Mickey Adams told the club's website: "We're delighted to bring both to the Vale. They are two vastly experienced midfield players, who will bring real competition for places in that department."
The 29-year-old Jennings joins the club after a successful trial, following his release from Tranmere, and Brown, 37, was a free agent after leaving Leeds.
Adams confirmed Brown will perform a dual role with the club, adding: "Michael will also combine playing with coaching the reserve team when fixtures permit."