Graham has admitted that he became frustrated with a lack of first-team opportunities at Hull, where he made just 18 appearances.
"I've got time to make up after what has been the most frustrating year of my career. I wasn't getting starts at Hull and I'm not a player happy to sit on the bench and pick up money, I want to play," he told the Evening Gazette.
"But I'm fit and hungry for it so hopefully it won't be long before I am showing what I can do. I know what to expect. I know how hard it can be, how hard you need to work to get chances but I'm looking forward to it.
"I can't wait to start helping Boro win games and climb the table."
Graham scored once during his time with Hull.