Courtois, 26, has signed a six-year deal to join the Champions League champions.
Courtois joined Chelsea in 2011 from Genk but was immediately loaned to Atletico Madrid for two seasons, before he returned to Chelsea to claim the first choice goalkeeping spot.
He joins the La Liga side for £35 million with Real Madrid midfielder Mateo Kovacic joining Chelsea on loan.
Chelsea have replaced the goalkeeper by signing Kepa Arrizabalaga from Athletic Bilbao after triggering his €80m release clause.
Courtois said at his unveiling: “Today I am realising a dream. This is the best club in the world.”
— Real Madrid C.F. (@realmadrid) August 9, 2018
He was voted the best goalkeeper at the Russia 2018 World Cup.
Chelsea have signed Kepa Arrizabalaga from Athletic Bilbao as Courtois’ replacement for £71m – a world record for a goalkeeper.
Follow the live updates of the completed deals, news and gossips from the Premier League #DeadlineDay here