Griffiths joined ahead of the current season from Prescot Cables, and has previously played for Bolton Wanderers youth, Runcorn Linnets and Warrington Town.
Manager Neil Reynolds said: "It gives me enormous pleasure to be able to announce that Luke has decided to sign a contract and commit his future to the club, we’ve been trying to get this deal over the line for the last three weeks.
"Naturally Luke’s attracted a lot of attention from other clubs higher up the pyramid than FC but we’ve talked to him a lot over the last few weeks and he’s decided that his future lies here.
"From the first day he came in at pre-season he’s just lit things up, his attitude is impeccable, he’s a real favourite in the dressing room and his performances have certainly done the talking so it’s incredibly pleasing."
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