The 29-year-old secured his switch to White Hart Lane in the final hours of the transfer window after his proposed move to Liverpool ended due to the Anfield club's unwillingness to match the forward's £7 million valuation.
Reds boss Brendan Rodgers has since admitted he believed his side were going to push through a deal for the Fulham man.
"We are happy that this whole thing was finalised, that he got the move to a real international club that is always competing in the top four or six of the Premier League," Klinsmann told reporters. "I personally, I'm excited because I played for Tottenham many, many years ago. It gives me me a chance to watch one of his games in one of my old places.
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Klinsmann has called Dempsey into his 24-man squad which will face Jamaica twice in four days in World Cup qualifying. The first match is on September 7 in Kingston, Jamaica. With Dempsey having not playing in a Premier League game this season, the USA boss admits he will assess the forward before making his selection.
"We'll evaluate him. We'll sit down with him," Klinsmann said. "We'll discuss his state of mind and also obviously we'll test his fitness level right away when he comes in to see where he's at in order to help him. If he's lagging behind then we'll know exactly where he's at and we can help him to catch up as quickly as possible."
With Landon Donovan and Michael Bradley missing out through injury, Klinsmann has revealed Dempsey could be handed a start: "We're absolutely open to throw him in the water right away.
"It really depends on where he's at, if he's in a very good physical level," Klinsmann said. "He worked out with the fitness coach of Fulham on the side. They did one-on-one work, which is often more effective than team training."