Graham is relishing the opportunity to get his top-flight career back on track after sealing a one-year loan move to newly-promoted Hull.
He told the Tigers' official website: "It's great to come to a club where everybody is on a high after winning promotion and I've only heard good things about this club.
"It's exactly the same as when I joined Swansea a couple of years ago, a club coming up into the Premier League. The stories for two clubs are very similar.
"I know I'm coming to a good club with a top manager, a fantastic stadium and some very good players."