The former England centre-half is excited about launching his second spell with Boro following his £7m capture from Real Madrid in 2007.
"The pull of helping Boro back in the Premier League is very strong for me," said 32-year-old Woodgate, who saw regular action with Premier League Stoke City last season. "And from what I have seen of the current squad, I think it's achievable.
"Tony Mowbray explained his plans for next season and how he is building a team that wants to get back in the Premier League as soon as possible. I want to be part of that and if we can achieve promotion in my time here it will be a fantastic way to end my career.
"Tony also likes his teams to play football the right way, and that was also a big plus point for me. It's just a great feeling to come back to this football club."
Mowbray is delighted to have signed out-of-contract Woodgate following the arrivals of Grant Leadbitter, Stuart Parnaby and Christian Burgess earlier this summer.
"I've been very impressed with Jonathan in my conversations with him and his passion for the football club stands out," he said.
"I don't need to eulogise about Jonathan's quality. He's played for some of the biggest clubs in the world. We need to build on that experience and the quality he brings to our squad."
Woodgate spent a highly-successful 18 months at the Riverside following his move from Real Madrid, initially on loan. He played 46 games for Boro before moving to Spurs in January 2008.
He began his career with Leeds United and also had a spell with Newcastle United.