The American was linked with a move away from Craven Cottage throughout the summer, with Liverpool said to be his preferred destination, before agreeing a £6 million switch to Spurs on deadline day.
And Dempsey is delighted to have moved to a side where he will not only have the chance to play in Europe but also not need to unduly unsette his family.
He told The Guardian: "I'm very relieved and looking forward to getting back to playing.
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"But it's still in London. My family doesn't have to move far. My daughter, she can go to another international school and be on the same curriculum. It couldn't have worked out any better in that regard."
After netting 23 times in all competitions for Fulham last season, Dempsey had made no secret of his desire to play for a Champions League club - and, despite that not being the case for Tottenham this season, he believes that there is sufficient quality within the side to do so in future.
"I always wanted to play at the highest level possible. That was never a secret. That's something I always said," he asserted.
"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."
After five years at Fulham, Dempsey concedes that he was disappointed to leave on sour terms after refuting reports suggesting that he refused to play but is now looking forward to his career at Tottenham.
"I'm disappointed in the way I was portrayed in the end with Fulham," he continued.
"There were some things that were said that weren't true. That's in the past. It's about looking towards the future. 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."