Antonio Rudiger claimed “it was Real Madrid or nothing” during his official unveiling on Monday.
The 29-year-old refused to sign a new deal with Chelsea and left as a free agent.
Rudiger has now put pen to paper on a four-year deal at the Santiago Bernabeu.
“It’s a very special day for all of us, but especially for me.
“I would like to thank my parents, because without them I could not be here. They have always supported me and that throughout my life has been very very important.
“I also want to thank the president of Real Madrid for giving me the opportunity to play for this great club. I can promise you that I will give everything for this club. I want to win as many titles as we can. Hala Madrid and nothing else!” Rudiger said.
Rudiger also confirmed that Barcelona showed an interest in signing him, but he told his brother, who is his agent and advisor, that it was “Real Madrid or nothing”.
The German defender will earn £315,000-per-week in Madrid, significantly more than the £230,000-per-week deal Chelsea were offering him.