Woodgate held talks with Spurs over the weekend after they agreed an undisclosed fee with Boro for the 28-year-old defender.
The former Leeds United man was given permission to talk to Spurs and Newcastle after Boro accepted offers from both sides.
However, Newcastle boss Kevin Keegan conceded on Saturday that Woodgate would not be making a return to St James' Park as he had opted to go elsewhere.
Spurs are believed to have offered Woodgate a three-and-a-half year deal at White Hart Lane.
Woodgate is set to tie up his transfer to the north London club on Monday and he will become Juande Ramos' second signing of the month following the capture of Chris Gunter from Cardiff.
