The Germany international's current contract at Stamford Bridge is due to expire at the end of June, and he will not be signing an extension at Stamford Bridge amid the club's off-the-field issues.
There has been a host of speculation surrounding the defender's future in recent weeks, with a number of clubs, including Manchester United, Juventus and Paris Saint-Germain, believed to be keen to sign him on a free transfer this summer.
However, Real Madrid have recently emerged as the favourites for the centre-back, who is allegedly heading for Bernabeu this summer.
According to Italian journalist Fabrizio Romano, the move is now complete, with Rudiger agreeing a four-year contract at Bernabeu, although an official announcement will not arrive until the end of the season.
Romano claims that the 29-year-old has already undergone his medical with Real Madrid, who will make a statement after the Champions League final against Liverpool.
Sky Sports News report that the German's contract with the European giants will be worth in the region of £342,000 a week until June 2026.
Meanwhile, it is alleged that both Rudiger and his agent Sahr Senesie will receive a sizeable signing bonus, which could potentially be worth in the region of £30m.
Sanctions placed on Chelsea owner Roman Abramovich mean that the club are still unable to renew contracts, and their issues have played a key role in the central defender deciding to seek pastures new.
Rudiger has been a key player for the Blues since Thomas Tuchel's arrival as head coach, while he has starred during the 2021-22 campaign, making 50 appearances in all competitions, contributing five goals and four assists in the process.
Since arriving at Stamford Bridge from Roma in July 2019, the centre-back has scored 12 times and registered seven assists in 199 appearances in all competitions.
Rudiger has recovered from a groin problem to feature in Chelsea's last three Premier League matches, and he will have a maximum of four more games for the capital giants, including the FA Cup final against Liverpool on May 14.
Real Madrid allowed both Raphael Varane and Sergio Ramos to leave Bernabeu last summer, with David Alaba making the move to the club on a free transfer, while Eder Militao has played a prominent role for the La Liga champions this term.
Ancelotti's side secured the Spanish title at the end of last month and are now looking ahead to the Champions League final against Liverpool, with the club looking to win the competition for the 14th time.
Nacho has also again been a regular for Los Blancos this term, while Jesus Vallejo has featured in recent weeks, but the club have been short of centre-back options during the current season and have moved to secure Rudiger's signature on a free transfer. body check tags ::