The 27-year-old was offered fresh terms by the Baggies, but Jones opted to leave The Hawthorns, despite having a regular spot in the first team last season.
The defender will become an official Sunderland player on July 1 after agreeing a four-year deal following a free transfer to 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 the club'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."
Jones spent three years with West Brom, who escaped relegation from the Premier League last season, alongside Sunderland.