Los Blancos bought Kovacic from Inter in the summer of 2015 for 30m euros, with the Croatian being just 21 years old at the time.
The 25-year-old has penned a five-year deal at Stamford Bridge and is likely to be their only addition this summer due to the 12-month Federation Internationale de Football Association transfer ban.
Chelsea are now banned from registering new signings until the summer of 2020 after being found guilty of breaching rules when signing youth players.
"Mateo proved what an accomplished player he is during his season on loan with us", she said.More news: U.S. border patrol divers search for missing two-year-old girl in Rio Grande
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Despite facing a transfer ban, they are able to complete the permanent signing because Kovacic does not have to register as a new player.
They may be the only incomings at Stamford Bridge for the foreseeable future, although Chelsea have lodged an appeal against their transfer ban to the Court of Arbitration for Sport.
Kovacic will be left to fight for his place but the former Inter Milan man has experience of that, having been rotated heavily last term with Ross Barkley by ex-boss Sarri. Higuain arrived from Juventus in January and the Blues had the option to extend his loan deal for €18m (£16m/$20m) or sign him permanently for €36m (£32m/$41m).
He has now completed a permanent move, with the Blues expected to appoint Frank Lampard as their new manager in the coming days.