Graham joined Hull on a season-long loan on Friday following talks with Paolo Di Canio that revealed the 27-year-old was unlikely to feature for Sunderland under the Italian in the upcoming campaign.
Martin O'Neill was in charge when the former Middlesbrough, Carlisle United and Watford forward moved to Sunderland from Swansea City in January.
Under O'Neill and Di Canio, Graham failed to score in 13 Premier League appearances, but he is focusing on masterminding a change of fortunes at the KC Stadium.
He told TheHull Daily Mail: "I want to play games and Hull City have given me that chance to do it in the Premier League.
"I need to repay the faith the manager has shown in me where others might not have.
"Hull have taken a chance on me and I want to repay them with some goals and good performances.
"I felt I needed to get out of Sunderland. I spoke with the gaffer and he said I was going to be third or fourth-choice striker.
"I'm 28 in August and I don't want to be sitting around just picking up money.
"It's like a second lifeline for me. I had a good season with Swansea in the first year but then found myself out of the team for whatever reason.
"I moved on but that didn't work out. These things happen in football so this is a fresh start. I'm delighted to be here."
