Graham, 27, has signed a three-and-a-half-year deal to become Martin O'Neill's third signing of the transfer window following Kader Mangane and Alfred N'Diaye.
“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."
The striker - who started his career with Middlesbrough - joined Swansea from Watford in the summer of 2011 and went on to score 15 goals in 54 Premier League appearances.
The arrival of manager Michael Laudrup and new signing Michu resulted in a dramatic reduction in his first-team chances this season.
Graham was booed when playing for Swansea against Sunderland on Tuesday night as he was raised a Newcastle fan. He admits he may have to win his new supporters over.
The striker, born in Gateshead, said: “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.”
(source : http://uk.eurosport.yahoo.com)