The 25-year-old has penned a five-year deal at Stamford Bridge and is likely to be their only addition this summer due to the 12-month Fifa transfer ban.
He initially moved to West London from the Spanish capital a year ago and featured 51 times under previous boss Maurizio Sarri.
The ex-Dinamo Zagreb and Inter Milan midfielder failed to hit the net for the Blues but did help them to Europa League joy.A statement from Madrid, who he spent three years at, said: “Real Madrid CF and Chelsea FC have agreed to the transfer of player Mateo Kovacic.
“The club thankS Kovacic for all these years of dedication, professionalism and exemplary behaviour, and wishes him good luck in his new club.”
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