The deal, reportedly worth £40m, could be the Blues only transfer for the summer, due to a two-window transfer ban.
The west London outfit was able to sign Kovacic permanently because he was still registered with them after spending last season on loan at Stamford Bridge.
"I really enjoyed my season on loan with Chelsea, I feel comfortable at the club and like London and the Premier League very much," he said in a statement. "I am very happy to be able to join permanently.
"We had a successful year, winning the Europa League and I hope I can make a big contribution in the coming seasons."
Kovacic has penned a five-year contract with his new club.