The 28-year-old's four-season association with Whitby Town has come to an end after is was agreed to mutually end his contract.
Joining the Seasiders in 2021 from Blyth Spartans, Griffiths has been a regular in the side and went on to amass 124 competitive appearances, scoring on four occasions.
He has now penned a deal with the Steelmen, who are in the Northern League Division one and are managed by Carl Jarrett, assisted by former Seasiders Lee Bullock and David McTiernan.