Chelsea have bid farewell to Antonio Rudiger after the German defender departed on a free transfer.

The centre-half chose not to renew his contract with the club, despite several offers in the past year.

Rudiger has officially joined Real Madrid, with the European and La Liga champions announcing his arrival.

"We bid farewell to Antonio Rudiger as he departs Stamford Bridge with his Chelsea contract expiring, bringing to a close his five trophy-filled years with the club," Chelsea said in a lengthy statement.

"The German defender has left the Blues to join Real Madrid, having played a huge role in our successes in recent seasons. Rudiger lifted the FA Cup, Champions League, Europa League, UEFA Super Cup and FIFA Club World Cup with Chelsea, playing a crucial role in all those triumphs at the heart of our defence.

"The 29-year-old was also an important figure in the dressing room with his leadership and passion, while his dedication and desire to win never faltered, even when it became clear he would be leaving the club this summer."

Chelsea added: "Rudiger made 54 appearances in all competitions in his final campaign, all from the start, more than any other Chelsea player. 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.

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