The 27-year-old full-back will become a Sunderland player on July 1 after his contract at The Hawthorns expires.
Jones joined West Brom from Preston North End in 2011 and established himself as a regular with the Midlands club, making 74 appearances in his time in the Midlands.
However, after narrowly avoiding relegation with West Brom last season, Jones is relishing a new challenge at the Stadium of Light.
"I'm really happy to be here and I'm looking forward to getting back for pre-season and kicking on," Jones told Sunderland's official website.
"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."
West Brom director of football administration Richard Garlick revealed that they had been in negotiations with Jones with a view to renewing his deal, but are exploring alternatives following his decision to reject a final contract offer.
"Following further talks with Billy's representative, we made our final offer last week - a long-term deal on vastly improved terms based on Billy's contribution over the past three years," he told West Brom's official website.
"Billy rejected this and has exercised his right to run down his contract with a view to joining Sunderland.
"We're obviously disappointed by Billy's decision but wish him well in his future career.
"With there being no guarantees that Billy would re-sign, we have been preparing for this scenario and will pursue the options we have been exploring in the right-back position."
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