The 24-year-old spent the final six weeks of last season on dual registration from Hallmark Security League outfit AFC Liverpool, and played seven times in the league.
Jones has been on trial with the club throughout the summer, starting in the recent matches against Newcastle United, Nelson and Consett.
The Liverpudlian has spent time at Rochdale, AFC Telford United and Stockport County during his career, and he kept goal in Avenue’s victory in the West Riding County Cup final in April.
He becomes the eleventh member of Alex Meechan’s squad, and is only the second survivor from last season alongside Luke Dean.