Redshaw, 31, follows in the footsteps of father Ray, who had a spell with the Tigers in the 1982/83 season.
He said: ''I'm happy to have joined and can't wait to get started and prepare for the new season.”
Redshaw has scored 83 career goals in 274 appearances for the likes of Morecambe, Salford City and Halifax.
Hyde boss Nick Spooner added: “We're really pleased to have Jack on board, he's an excellent talent with great qualities and will add a further dimension to our squad.”
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