Liverpool had courted the player for much of the summer with Fulham making a formal complaint to the Premier League about what they claimed was an illegal approach for Dempsey from the Anfield club.
There were even reports that the 29-year-old had effectively gone on strike and the forward did not appear in either of the Cottagers' opening two fixtures of the season.
Dempsey said: "I'm disappointed in the way I was portrayed, in the end, with Fulham.
"I always wanted to play at the highest level possible. That was never a secret. That's something I always said.
"It would be a dream of mine to play Champions League and you want to play on the best team possible to try to get there.
"That's definitely a team with a lot of quality in it, but now it's all about the team that I'm with."
He added: "There were some things that were said that weren't true.
"That's in the past now. It's about looking toward the future and like I said, I'm looking forward to playing with Tottenham. It's a great team, a great club.
"I want to thank the fans of Fulham. It's been five great years.
"Some of my best memories in football have been there. I want to thank the chairman for talking a chance on me from MLS and I wish them well in the future."
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