Cribley returns to the club after building a career with spells in the USA at Syracuse University and with Barrow, Matlock Town and Mickleover Sports in the Northern Premier League.
Manager Gavin Smith said: "Ted came through our Under 19s and Reserves programme when Chris Dolby and I were in charge a few years ago. He’s got bags of talent and can score goals.
"We are looking forward to Ted making a big contribution as we look to push on an get back into a play off position."
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