The Black Cats' forward Stern John, 30, has moved in the opposite direction.
Jones became Roy Keane's third signing of Wednesday after Ian Harte (free) and Danny Higginbotham (£3m from Stoke) completed moves to the Stadium of Light.
Keane told his club's website: "I'm delighted that Kenwyne is a Sunderland player. He was very keen to join this club and that is always a good thing.
"He is a big strong boy who is quick and athletic too. He has real physical presence and is the type of player we've been missing."