The Driffield-born 25-year-old has been a life-long fan of the Tigers, and Posh owner Barry Fry has decided not to stand in his way of making a dream move to the KC Stadium any longer.
City initially went for Woodhouse last summer, but wouldn't meet Peterborough's six-figure asking price. They are now willing to let him go for what Fry describes as "a very reasonable fee" after being relegated to League Two.
This leaves an uncertain future for Ian Ashbee and Junior Lewis, who are both out of contract this summer and will see Woodhouse as direct competition for their places, although Peter Taylor has previously said that he'd like to agree new deals to keep the pair in his squad.