Kovacic will join Chelsea on loan until June 30, 2019 as part of the deal, with the Croatia worldwide spending a season away from the club he joined from Inter Milan in 2015.
Chelsea have informed Athletic Bilbao goalkeeper Kepa Arrizabalaga that they are prepared to pay his €80 million (£71.5m) buyout clause with the player set to make a decision about his future in the coming hours, sources have told ESPN FC.
With Thibaut Courtois joining Real Madrid, Chelsea signed 23-year-old Arrizabalaga as an instant replacement for the Belgium worldwide.
Courtois had just one year left on his contract and made clear his desire to return to Madrid, where he spent three seasons on loan with Atletico, to be closer to his two children.
Arrizabalaga becomes the most expensive goalkeeper in football history, ahead of Liverpool's Alisson, who moved from AS Roma for 75 million euros earlier in the transfer window. The Brazilian was Chelsea's first choice to replace Courtois, but he was keen to work with Jurgen Klopp.
Chelsea open their Premier League campaign at Huddersfield on Saturday, having suffered a 2-0 defeat to Manchester City in the Community Shield last weekend.
He helped the Blues win two Premier League titles, one FA Cup and one League Cup during his time at Stamford Bridge.
The deal that sees Courtois join Real Madrid for a reported £35million sees midfielder Mateo Kovacic head the other way on a season-long loan.