The 27-year-old has penned a three-and-a-half year deal at the Stadium of Light after falling down the pecking order under Michael Laudrup at Swansea.
The Englishman, who will wear the number nine shirt, becomes Martin O’Neill’s third signing of the January transfer window, following the arrivals of Alfred N’Diaye and Kader Mangane earlier this month.
And O’Neill is confident the former Swans man will be a success at the Black Cats, with Graham, who scored 12 Premier League goals last term, set to partner Sunderland’s prolific Scotland international Steven Fletcher.
“We’re delighted to have Danny and I genuinely think he’ll do well for us. He has a real desire to do well,” O’Neill told Sunderland’s website.
“I saw him from afar last season when he played very well in a system which seemed to suit him.
“I think he can fit in and score a few goals for us. We want to be less reliant on Steven Fletcher scoring the goals and I think Danny will alleviate the load.”
Meanwhile, Sunderland also confirmed that Louis Saha has left the club after the striker’s contract was ended by mutual consent.
Black Cats chief executive Margaret Byrne said: “We wish Louis all the very best for the future and thank him for his contribution to Sunderland.”
The former French international made two starts and a total of 14 appearances in the league and cup since joining the club in the summer of 2012.