The German international becomes a free agent at the end of this month and will head to the Santiago Bernabeu when his contract expires.
Rudiger is joining the team that knocked him out of the Champions League last season.
Chelsea met Madrid in the quarter-final of the competition but were defeated by the Spanish giants in dramatic fashion. Madrid went on to win the entire thing, beating Liverpool in the final in Paris, and also managed to win La Liga by 13 points.
And they are hungry for more.
Los Blancos are defined by their relentless ambition and that is no doubt what attracted Rudiger to the club. He is also a Champions League winner, having lifted it with Chelsea in Porto in the 2020/21 season.
The 29-year-old – with 52 German caps to his name – brings experience and bite to Madrid. He also brings a winning mentality he believes will fit the club like a glove.
“Yes, it is pressure [to be expected to help Madrid win a 15th Champions League],” he told Marca. “But this is the history of Real Madrid. They are used to winning and the mentality is exactly that – winning. But this winning mentality goes with my character.”