The midfielder joins from Prestwich Heys, where he spent a short time after leaving Bury FC.
Jones-Griffiths previously came through the youth system at Bolton Wanderers, where he worked under the guidance of Tigers boss Nick Spooner.
He has also spent time at Glossop North End and Congleton.
Following his arrival, Spooner said: "Shak is a player I have known since he was 11 years old, as I coached him at Bolton.
"He will add energy to our midfield, and I look forward to working with him again."
Photo credit: Hyde United
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