The 24-year-old Kovacic was part of Croatia’s run to the World Cup final, where it lost to France. Kovacic has been at Madrid since 2015, joining from Inter Milan.
Chelsea has also sold a player — goalkeeper Thibaut Courtois — to Real Madrid. The Belgian was replaced by Kepa Arrizabalaga after Chelsea met the goalkeeper’s 80 million euro ($120 million) buyout clause from Athletic Bilbao on Wednesday.
The transfer window is closing a day before the season opens on Friday with Manchester United hosting Leicester. United manager Jose Mourinho says he is “not confident” of signing players Thursday.