Woolford, 33, has spent the past two seasons with the Mariners, scoring five goals in 66 appearances.
He has enjoyed a stellar career in the Football League, playing for Scunthorpe, Bristol City, Millwall, Sheffield United and Fleetwood Town.
Tigers boss David McGurk, who played alongside Woolford at York City, said: “I’ve known Martyn a long time and he’s had a fantastic career. He’s still good enough and young enough to play in the football league and we are delighted that he’s here.
“He played 35 games in League 2 last year and he will provide invaluable experience to our young squad.”
Joining Woolford at Ewen Fields is a man at the other end of his career, young Huddersfield Town defender Oran Thompson.
Thompson, 19, has signed for Hyde on loan after penning a new professional deal with the relegated Premier League club in the summer.
McGurk added: “Oran has played in pre-season for us and he’s has been outstanding. He’s another young player with an awful lot of potential and we hope to help him realise this.
“He’s very mature for his age and I’m sure he will have a good career in the professional game. I would like to thank Huddersfield Town for allowing us the opportunity to work with Oran.”
Hyde open up the BetVictor Northern Premier campaign at home to Basford United on Saturday.
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