The 28-year-old becomes Black Cats boss Roy Keane's first summer signing and has penned a three-year contract. Spurs fullback Pascal Chimbonda is also set to sign with the Black Cats.
Versatile midfielder Tainio and full-back Chimbonda have both revealed how impressed they were with Keane at the weekend.
Chairman Niall Quinn and chief executive Peter Walker have managed to push through the first of the deals ahead of Keane's return with his squad from their pre-season camp in Portugal on Thursday.
Keane said on the club's official website: "I'm delighted to sign a player of Teemu's experience and quality, he'll be a valuable addition to our squad.
"Teemu has showed versatility, playing in different midfield positions for both Tottenham and his previous club, Auxerre.
"But his experience in particular and the fact he has played more than 40 international games shows he has a lot to offer Sunderland."