The former Bayern Munich midfielder completed his move last week.
"I wanted a change," Kroos said.
"The first time I gave it any thought was when contract talks with Bayern hit the buffers. Bayern were always my first contact and that is why I had always ruled out making contact with any other clubs.
"When we were unable to reach an agreement and several interested clubs, including all of the biggest clubs in the world, approached me, I decided to try out something new.
"Winning the World Cup then tipped the scales."
He insists his decision to join Madrid was made in favour of the Champions League holders and not against Bayern.
"I have played in one of the best clubs in the world, and was a regular under many different coaches in recent years and I was always able to feature, despite the fierce competition," Kroos added.
"I was always taken excellent care of at Bayern too. Pep Guardiola and director of sport Matthias Sammer were always important people whom I could talk to and they showed their faith in me.
"And the fans always supported me too, and I thanked them on my homepage immediately after my transfer.
"My aim was to experience something new."
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