The England U21 hitman completed a £1.5m move to Spurs from Brighton this afternoon.
Still just 22, Zamora bagged 76 goals in 123 appearances for the Seagulls in the Nationwide League.
"I can't wait to get out there," he said pitch-side at the Lane. "It's been a hectic 48 hours but I'll take my time, pinch myself a little and start to enjoy it.
"I'm looking forward to the start of the season. Pre-season is here already and I can't wait to get out there playing again."
Zamora's arrival ended months of speculation linking him with the club.
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He revealed: "I knew Spurs had been coming to watch me for quite a long time and initially it was at the back of my mind but eventually I though they'll either sign me or not. I stayed relaxed and made sure I enjoyed myself.
"Now I'm here I've a simple target - play a few games and score a few goals.
"It will be tough to step up but I'm young and I will learn. Hopefully it will all come good and I'll score goals for Tottenham."
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Bobby Zamora took a look around White Hart Lane and admitted: "I can't wait to get started."