Spurs revealed that the United States captain was returning to Major League Soccer after just one season at White Hart Lane.
And the Sounders have 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."