Kovacic was allowed to join Chelsea despite their transfer ban.
Midfield ace expresses delight at signing for west London club.
Chelsea have signed midfielder Mateo Kovacic on a five-year deal from Real Madrid.
The Blues were given permission to sign the midfielder despite their transfer ban because he was still registered to the club until the end of June following his loan spell from Los Blancos.
"I really enjoyed my season on loan with Chelsea, I feel comfortable at the club and like London and the Premier League very much. I am very happy to be able to join permanently," Kovacic said as Chelseafc.com quoted.
"We had a successful year, winning the Europa League and I hope I can make a big contribution in the coming seasons."
According to widespread reports, Chelsea agreed a fee of 45 million euros (£40.25m) with Real Madrid for the 25-year-old.
A Real Madrid statement read: "The club wants to thank Kovacic for all these years of dedication, professionalism and exemplary behaviour, and wishes him good luck in his new stage."