Goal.com revealed the former Swansea City striker was set to complete his move to the Stadium of Light after his preferred move to Newcastle United failed to materialise.
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Martin O'Neill snapped the 27-year-old up on deadline day on a three-and-a-half year contract.
"As soon as I heard about the interest from Sunderland I didn't even have to consider any of the other options that were on the table,” he told the club's official website.
"I was born and brought up in the north east so I know first-hand the intense passion that people have for their football in this part of the world – it's special and there's nowhere else like it."
Graham, born in Gateshead, was raised a Newcastle supporter but insists he is totally committed to the Sunderland.
"Of course, I totally understand that some fans might need convincing about my commitment to Sunderland because of my roots, but I've always given 100 per cent no matter what team I play for and no matter who I play against.
"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.
"I'm really excited about the future – this is a new phase of my career and I can't wait to get started."
Graham joins fellow new arrivals Alfred N'Diaye and Kader Mangane at Sunderland and will wear the No.9 shirt.