The 28-year-old former Leeds United and Real Madrid stopper was also a target for another of his former clubs, Newcastle United, but Woodgate has opted to head for White Hart Lane.
He joined Boro, initially on loan, in the summer of 2006 and has gone on to make just over 50 appearances for the Teessiders.
Newcastle had given up their pursuit of the defender at the weekend, with boss Kevin Keegan admitting: "At this moment I don't think he is going to come to Newcastle.
"In fact I am almost certain he isn't. I think he is going to go somewhere else.
"It looks like we have lost him. I am very disappointed. I fully understand, but I desperately wanted him to come."
Boro boss Gareth Southgate spoke of his disappointment at losing Woodgate, telling the club's official website: "You're looking for everyone at your club to want to be here and be part of it.
"We wanted to give Jonathan the opportunity to speak to other clubs because when clubs call you about a player it usually means the player knows about it anyway.
"We were then asking a question of Jonathan, do you want to be here and be part of what we want to do or do you want to head off? And it seems he wanted to head off."