The Driffield-born player has only been with City since the summer, joining in a dream £25,000 move back home. However, he has failed to become a big part of Peter Taylor's plans, and the last of his 15 starts came two months ago.
Former England Under-21 international Woodhouse denied that there was a rift with manager Taylor, and chairman Adam Pearson says the transfer is for footballing reasons.
He told the Hull Daily Mail: "The move will give him first-team football which is something we couldn't guarantee him.
"We wish him all the best for the future. It hasn't worked out here."
Woodhouse follows Roland Edge, Marc Joseph and Jason Price in leaving the club in recent weeks. Stuart Green has turned down a move away after an offer was accepted from Milton Keynes Dons. Interest from Chester to take Kevin Ellison back to the Deva Stadium has been rejected.