The two players joined Spurs from Fulham within a day of each other, with Dempsey completing his transfer just before the 11pm deadline on Friday.
Dembele believes that the American will be a success at White Hart Lane, and is also happy that he won't have to play against him in the Premier League.
"Clint always is so dangerous," Dembele said.
"I sent him a message saying I was very happy because he is a fantastic player. He is a good boy so I am very happy that he is here. He is so hungry to score goals. He fights a lot and it is fantastic to have him in the team.
"He works as hard as two men so I'd prefer to have him in my team rather than play against him."
Dembele scored on his Spurs debut at the weekend as they drew 1-1 with Norwich City.