The German international is nearing the end of his contract with the Premier League club, and he has refused to sign an extension with the Blues so far.
The defender has signed a 4-year contract with Real Madrid, and he will earn around €9-10m per season.
Furthermore, the player will have a €400m release clause in his contract, and he has already undergone his medical with the Spanish club.
Reports claim that the transfer should be finalised and announced after the Champions League final.
Real Madrid takes on Liverpool in the Champions League final on the 28th of May.
Rudiger has been an outstanding servant for Chelsea since joining the club, and he has been a critical player for Thomas Tuchel. It will be interesting to see how the Blues replace him next season.
Chelsea are expected to lose the likes of Andreas Christensen as well.
Thomas Tuchel will require significant reinforcements at the back this summer if Chelsea are to challenge for the Premier League title next season.
The likes of Cesar Azpilicueta and Thiago Silva are in the twilight years, and the Blues must bring in more than one centre-back this summer.
The likes of Jules Kounde have been linked with a move to Stamford Bridge, and it’ll be interesting to see who they end up signing eventually.