The 29-year-old will move to the Bernabeu on a free transfer after he turned down the Blues' attempts to renew his contract.

Sky Sports News reported last month Rudiger was set to join Real after choosing the newly-crowned European champions over a host of other elite clubs, including Paris Saint-Germain, Juventus and Manchester United.

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It was reported at the time that the Germany international's new deal would be worth €400,000 (£340,000) per week.

Real say they will present Rudiger as their player at a ceremony on June 20.

Writing on Twitter, he said: "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."

Chelsea added: "Chelsea Football Club thanks Toni for his contribution to our success over the last five years and wishes him well in his future career.

"He departs with 203 appearances and 12 goals to his name, in that time establishing himself as one of the most passionate characters to represent the club in recent memory."

Rudiger joined Chelsea from Roma five years ago, and won the 2018 FA Cup in his first season at the club under Antonio Conte.

He then helped the Blues to Europa League glory in 2019 under Maurizio Sarri, but struggled for games under the Italian's successor, Frank Lampard.

Rudiger was attracting interest from clubs looking to take him on loan in January 2021, until Lampard was sacked and replaced by Thomas Tuchel, who immediately restored his countryman to the starting XI.

The former Stuttgart and Borussia Dortmund defender was instrumental in Chelsea's Champions League success at the end of the 2020/21 season, as well as their Club World Cup win earlier this year.

Chelsea eyeing Kounde after takeover confirmed

Sky Sports' senior reporter Melissa Reddy:

With Rudiger's departure finally confirmed, and his fellow centre-back Andreas Christensen also set to move to La Liga, Chelsea are now pressing ahead with their summer recruitment plans.

The £4.25bn Todd Boehly-led consortium takeover of the club was completed earlier this week, which should allow Thomas Tuchel to begin building his squad for the upcoming campaign, with centre-back certain to be an area of concern.

The Blues have a verbal agreement already in place with Sevilla defender Jules Kounde, with the Spanish club preferring a quick deal as they aim to balance their books before June 30.

Talks on a deal for Kounde had collapsed last year but there is optimism from all parties it will get done this time.

Paris Saint-Germain's Presnel Kimpembe is part of a shortlist of central defensive options and is Tuchel's preference. Atletico Madrid's Jose Gimenez and RB Leipzig's Josko Gvardiol are also among those being looked at.