The Barclays Premier League side had earlier revealed that the United States captain was returning to Major League Soccer after just one season at White Hart Lane.
The Sounders confirmed the deal, with majority owner Joe Roth telling his club's official website: "This is a historic day for Sounders FC and our fans. Clint is a world-class soccer player who can take this club to a higher level."
Dempsey was paraded in front of the Sounders' support before their home match against Dallas at CenturyLink Field.
Roth continued: "We have been consistent in our message to the fans that we will spare no expense to win trophies."
Owner and general manager Adrian Hanauer added: "In doing something of this magnitude we had to make sure we had the right player. Clint Dempsey fits that mould.
"He is a proven winner, a leader and a competitor who we believe will raise the bar for this organisation on and off the field."
Dempsey joined Tottenham from Premier League rivals Fulham on transfer deadline day last summer for around £6million, scoring 12 goals in 43 appearances for the north London club.
The 30-year-old first made a name for himself playing for the New England Revolution before joining Fulham in 2007.
Dempsey himself said: "I am very excited about coming back to the MLS and thrilled to be joining Sounders.
"Having recently played in Seattle with the national team, I experienced the incredible atmosphere and the passion from the supporters first-hand. It's going to be an honour to represent the fans in Seattle."