The German international completed his move to the European Champions on Thursday for a fee believed to be in the region of £24m.
Kroos had been linked with a number of clubs in recent months, but he has claimed that the only team he wanted to play for was Madrid.
"It made me very happy, I was very proud. I'm absolutely convinced that it's the right choice and today just reaffirmed my decision," he told Real Madrid TV.
"Everyone has been very friendly towards me, I've liked everything so far. Meeting the fans was very special and reaffirmed to me that I've made the right decision.
"In my opinion, Real Madrid are the biggest club there is. That's why I was sure I wanted to join them. They were my first and only choice and everything went according to plan."
Kroos started each match in Germany's World Cup-winning campaign.