Kovacic's arrival is part of the deal which saw Chelsea keeper Thibaut Courtois join Real on Wednesday on a six-year contract. Real will pay an initial 35 million euros (31.5 million pounds) for the Belgian goalkeeper, Spanish media reported.
The 24-year-old Kovacic was part of the Croatia team that reached last month's World Cup final but was used almost exclusively as a substitute at Real last season.
"I am really happy and excited to be here at Chelsea. It is an amazing feeling," Kovacic said on Chelsea's website.
"I will try to do my best for this club. It is a new league for me, the beginning is always tough but I am sure the coach and my new team mates will help me and I am looking forward to a great season."
Central midfielder Kovacic broke through the youth ranks at Dinamo Zagreb and scored on his senior debut, aged 16.
He soon came to the attention of some of Europe's biggest clubs and joined Inter Milan in 2013.
After making 100 appearances for the San Siro club he joined Real in 2015.
(Reporting by Martyn Herman; editing by Sudipto Ganguly)
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