Jones has signed a four-year contract with Sunderland, having rejected a new deal with West Brom.
He told the club's website: "I'm really happy to be here and I'm looking forward to getting back for pre-season and kicking on.
"I've played at the Stadium of Light a number of times so I know what it's about and what great backing the club has.
"I've come to the training ground today and it's amazing. I knew I was signing for a massive club with everything in place to kick on up the league and carry on moving forward."
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