The 24-year-old becomes Chelseaâ€™s fourth summer signing, with the midfielder following Kepa Arrizabalaga, Jorginho and Rob Green to Stamford Bridge.
New Blues manager Maurizio Sarri is keen to bring in his own players before todayâ€™s 5pm deadline to freshen up his squad.
Speaking about his move to to Chelsea, Kovacic said: â€śI am really happy and excited to be here at Chelsea.
â€śIt is an amazing feeling. I will try to do my best for this club.
â€śIt 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.â€ť
Blues director Marina Granovskaia added: â€śWe are very happy to welcome Mateo to the Chelsea family.
â€śHe is a perfect fit for us this season, his style is well suited to how Maurizio wants to play and we are sure he will prove to be a valuable asset for the club.â€ťÂ
The Blues have had a busy couple of days in the transfer window, with Chelsea signing Kepa in a world-record deal yesterday.
Kepa, who becomes the most expensive goalkeeper of all time, will replace Thibaut Courtois at Stamford Bridge.
Belgium international Courtois went AWOL and refused to train with Chelsea in hope of forcing through a move to Real.
The Blues No 1 got his wish with Real expected to announce their new signing this afternoon.
Courtois, 26, will cost the Spanish giants around ÂŁ35m and heâ€™ll pen a six-year contract at the Bernabeu.
Kovacicâ€™s arrival is bad news for Chelseaâ€™s midfielders, with the Real Madrid manâ€™s arrival possibly reducing their amount of game time.
Nâ€™Golo Kante and Jorginho are expected to start in midfield for the Bluesâ€™ opening Premier League game against Huddersfield on Saturday afternoon.
That leaves Ross Barkley, Cesc Fabregas, Tiemoue Bakayoko, Danny Drinkwater and Ruben Loftus-Cheek worrying about their Stamford Bridge futures.
Chelsea are fully focused on domestic competitions this season after failing to qualify for the Champions League last time out.
On a positive note for the Blues, Sarri looks set to keep hold of Eden Hazard.
The Belgium has been tipped to quit Chelsea for Real in recent weeks.
However, Real are unlikely to make a move for the winger in the coming weeks, with their transfer window closing at the end of the month.
Chelsea face Huddersfield on Saturday afternoon (3pm kick-off).