The keeper was close to signing for Spurs in January but the deal was blocked because the club wanted to loan him back to Leeds for the rest of the season.
The 24-year-old told a news conference today: "It's a big wrench to leave Leeds because I've been there since I was 14, but they needed me to go and I needed to go to further my career.
"The decision was taken out of my hands. There has been a lot of uncertainty and I'm glad my future's finally settled. Leeds made it clear that everybody was for sale and if my transfer brings some money into the club it benefits everybody.
"It was very close to happening in January but I didn't want to leave Leeds in the predicament they were in, so the deal was put on ice until now."
Robinson said he consulted former Spurs player Nick Barmby and former White Hart Lane boss Terry Venables about Tottenham, where they had been together in the early 1990s.
"I spoke to Nick and Terry and they both told me Spurs is a massive club with great potential, and they seem to be going in the right direction. I did not take much convincing.
"The chairman has assured me that there will be more quality signings made this summer and a new manager, and we'll be looking for a UEFA Cup spot next season."