Hyde, signed by former Blues boss Trevor Francis from Sheffield Wednesday in 1999, had recently been on a two month loan deal at second division side Peterborough United and last season had a similar spell with Chesterfield.
"He's an experienced midfield player," said Rovers boss Ray Graydon.
"He'll be a valuable addition to our squad. I'm pleased to have him on board and absolutely delighted that he's agreed to join us.
"Graham will add competition for places and will bring in some experience to a relatively young squad."