World Cup finalist Kovacic has been pushing for a route out of the Bernabeu in recent weeks due to limited playing time, and having been granted his wish by Julen Lopetegui he is now raring to go at Stamford Bridge.
"I am really happy and excited to be here at Chelsea," he told the club's official website. "It is an amazing feeling. 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 teammates will help me and I am looking forward to a great season."
More than half of Croatia international Kovacic's appearances over the past three seasons have come from the bench.