The Gateshead-born striker had been looking to get away from south Wales and was always linked with a move to the north east, where Sunderland remained favourites despite interest from others.
His former club Middlesbrough had an offer accepted by Swansea on Thursday morning but his agent ruled out a return to his former club and instead he arrived at the Stadium of Light for a medical and to agree personal terms.
The boyhood Newcastle fan has now appealed for support from the Black Cats followers.
He told safc.com: “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.
“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.”
“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% 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.”
Stoke could face a battle to keep Xherdan Shaqiri as reports have claimed Mark Hughes wants him at Southampton next season.
Bayern Munich have entered the race to Emre Can, who continues to talk up a move away from Liverpool this summer.