Real Madrid have signed Belgian goalkeeper Thibaut Courtois from Chelsea with Croatia midfielder Mateo Kovacic going the other way on loan, the clubs said on Wednesday.

Courtois has agreed a six-year contract and Real will pay an initial 35 million euros ($40.7 million) for the Belgian goalkeeper, Spanish media reported.

"The Golden Glove (winner) from the last World Cup signs for the Champions League champions after his impressive performance in Russia," Real Madrid said in a statement.

"After his medical on Thursday August 9, the player will be presented in the presidential box at the Santiago Bernabeu."

The 26-year-old previously played for Atletico Madrid on loan from Chelsea for three years between 2011- 2014 and wanted to return to the Spanish capital, where his children live.

"I would like to express my heartfelt gratitude for the four fantastic years that have passed. Chelsea FC will always have a fantastic place in my heart," Courtois said on Facebook.

"I want to thank the fans for their great support over the years. I hope you understand that being closer to my kids was considerable in my decision."

Courtois played 154 times for Chelsea after arriving at Stamford Bridge in 2011, keeping 58 clean sheets.

British media reported that the Belgian, who has played 65 times for his country and helped them reach this year's World Cup semi-finals, has not shown up for training at Chelsea for the past two days in a bid to force through the transfer.

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