The 27-year-old made the move to the Stadium of Light from Swansea City for a reported £5m on deadline day.
Despite expressing his delight at signing for the North-East side, the forward was booed by the Black Cats fans during Sunderland's goalless draw with the Swans on Tuesday due to his allegiance with Newcastle United, whom he supported as a child.
"I am sure I can win over the fans with my attitude and performances on the pitch," the Daily Star quotes Graham as saying. "Of course, I totally understand that some might need convincing.
"But I've always given 100%, no matter what team I play for. It's up to me to show people I deserve to wear the Sunderland shirt and I'm excited about playing for a club as big as this."
Graham has been given the number nine shirt at the Stadium of Light.