The 27-year-old striker completed a £5million switch from Swansea yesterday afternoon, Black Cats manager Martin O'Neill finally getting the man he had been chasing throughout the transfer window.
Graham landed on Wearside with some fans questioning his Newcastle roots, but central defender Bramble was delighted to see him join the club.
He tweeted: "Very happy that Danny Graham has signed for us. A very good player who will score lots of goals for us. A great addition to the squad."
Gateshead-born Graham, however, will have to win over the section of the Sunderland support which booed him when he was introduced as a substitute during the Swans' 0-0 draw at the Stadium of Light on Tuesday evening.
Their antipathy dates back to a fanzine interview in which the boyhood Magpies fan was less than complimentary about his new employers.
However, Martyn McFadden, editor of Sunderland fanzine A Love Supreme, is convinced he will be accepted as long as he does well on the pitch, as was former Magpie Michael Chopra initially after scoring the winner against Tottenham on his debut in August 2007.
He said: "With Chopra, there were question marks over him and he scored on his debut against Spurs and the fans were singing, 'He's one of us'. Then when he failed, you have the finger being pointed at him.
"If he (Graham) succeeds, he will be welcomed; if he fails, he will be questioned.
"But he will earn himself a lot of money by pulling on that red and white shirt, and that's what a professional football does - he does his job for the club which pays his wages.
"He made some comments earlier in his career which he probably wishes he had never made.
"There's no avoiding the fact that he's Newcastle United fan, but there are not many players, if any, at the club who have an affinity historically with Sunderland Football Club.
"We have people from all over the world, none of whom had ever supported or had any interest in Sunderland Football Club before they started playing for it.
"What he said is unfortunate, but he will just have to work even harder and if he does that, he will be a success and the fans will be happy."
Graham knows he has bridges to build, but is confident he can prove himself to those fans not particularly enamoured with his capture.
He 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."