The goalkeeper has moved for a fee in the region of £31m and has signed a six-year contract.
Chelsea have taken Croatia international Mateo Kovacic on season-long loan from Real as part of the deal.
Kovacic, 24, told Chelsea’s website: “I am really happy and excited to be here at Chelsea. It is an amazing feeling. I will try to do my best for this club.
“It 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.”
Chelsea on Wednesday confirmed the signing of Courtois’ replacement; Kepa Arrizabalaga from Athletic Bilbao.
The Spain international, 23, has signed a seven-year contract at Stamford Bridge and joined the Blues for £71m – a world record fee for a keeper.