The 29-year old attacking midfielder ended his five-and-a-half-year stay at Craven Cottage when he sealed a £6million move to White Hart Lane on transfer deadline day and has spoken out about the reasons why he wanted to move on.
"It's an opportunity for me to play three more years guaranteed at such a high level and gives you an opportunity to see where you are and if you can make it," Dempsey told Sports Illustrated.
"For me, it's always been about being able to look myself in the mirror and say: 'You tried your best. You challenged yourself'.
"And you'll be able to die a happy man in the sense of your career, knowing that you were able to see if you could do it or not'.
"It is a gamble you take when you make a move to a new team. You don't know where you're going to fit in exactly. You don't know how you're going to gel.
"It will be interesting to see where I will fit in because I don't know what his (Spurs boss Andre Villas-Boas) plans are in that sense.
"I have to show him where I am at, obviously, and he will see what the best fit will be."