The German international played more than 200 times for the Blues and played a key part in their Champions League win last year.
However, he will leave the club on a free transfer after failing to sign a new contract with the west Londoners.
Chelsea boss Thomas Tuchel confirmed the sanctions imposed on the club and outgoing owner Roman Abramovich meant they were unable to tie Rudiger down to a new deal.
He has signed a four-year contract with the Spanish giants and European champions, fresh off of their Champions League final win over Liverpool.
He tweeted: “I’m proud to announce that I’ll be joining Real Madrid. I’m super excited for all the challenges ahead and can’t wait to play my first games for this huge club.”
Real have confirmed that the presentation ceremony to officially announce Rudiger as a Madrid player will take place on June 20.
A statement released by the club ends with: “Chelsea Football Club thanks Toni for his contribution to our success over the last five years and wishes him well in his future career.”
