According to the press service of the Madrid club, an agreement with the 29-year-old player has already been signed and is designed for four years.
The German's contract with Chelsea expires at the end of June, after which he will be able to join the Spanish team.
Rudiger moved to Chelsea in 2017.
Together with the London team, he won the Champions League, Europa League, UEFA Super Cup, Club World Cup and FA Cup.
In total, he has 203 matches, 12 goals and seven assists in the English team.
Earlier it was reported that Real Madrid offered midfielder Toni Kroos a contract extension for a year.