The 29-year-old joined Spurs in a £6m move after rejecting an offer from Aston Villa earlier in the day, with talks between the Cottagers and Liverpool breaking down in the evening.
"To play under this head coach (Andre Villas-Boas) and play for this club is a dream come true," Dempsey is quoted as saying by the BBC.
"I want to make the most of it. There are a lot of great players here, I'm looking forward to training and playing with them."
Dempsey joined Fulham from New England Revolution in January 2007.