The 21-year-old signed his four-year contract on Wednesday having passed a medical at the weekend - but will remain playing in the MLS season before joining the Premier League club for the 2015/16 season.
A Tottenham tweet read: "We are delighted to announce that we have reached agreement with Seattle Sounders for the transfer of DeAndre Yedlin."
Yedlin impressed at the World Cup as USA reached the knockout stages and further caught the eye of Tottenham manager Mauricio Pochettino in the 3-3 friendly draw with Seattle earlier this summer.
Yedlin told the club's website: "I’m very excited to come to the Premier League and challenge myself against some of the best players in the world.
"The facilities are the best in Europe, if not the world. It’s a great team. I’m very excited. It’s a great team with a new coach and a style that suits the way I play. That’s a big reason I made the decision."
He has seven caps for the USA under former Spurs striker Jurgen Klinsmann and has played 42 times in MLS for Seattle.
He made three appearances for the USA at the World Cup, in group games against Portugal and Germany and in their last-16 defeat to Belgium.
In another tweet on the club's Twitter account, Yedlin added: "I’ve talked to Jurgen Klinsmann a lot about this move and he supports it, which was one of the big reasons behind the decision."
The MLS regular season finishes on October 20, when the Sounders face LA Galaxy, before a post-season play-off that concludes with the final in December.