Here is how social media have reacted to the 26-year-old's move, with many tipping Barcelona's Lionel Messi to score goals aplenty when they face Madrid.
Liverpool are the window's biggest spenders so far, with boss Jurgen Klopp bringing in £160 million of new recruits, but the total spend by Premier League clubs is unlikely to smash the £1.4 billion record set in 2017. "If he ends up here one day, that would be brilliant". "They [the fans] will see that I'm going to give my all for Madrid".
Despite that, he has maintained regular playing time and has accumulated over 100 appearances during his three years with Real, including in the Champions League, which Real Madrid have won every season since Kovacic joined. If they'd done all a little sooner, I'm sure they would have saved some Chelsea fans' hearts.
"I am really happy and excited to be here @ChelseaFC". I just think Chelsea have made a great bet in taking me.
New Chelsea goalkeeper Kepa Arrizabalaga has urged Eden Hazard to stay.
Arrizabalaga, who made his full global debut for Spain against Costa Rica in a November friendly past year, will feel he has plenty to prove at Chelsea, as he attempts to live up to his remarkable price tag.
Sanchez had previously played in England with Aston Villa and he said: "I always maintained the same desire to return and here I am, with the same mission, with the same desire and dream". Only two keepers made more saves in the Liga last term, and he's pretty good with his feet too - once deployed outfield during an injury crisis for his U14 team, he scored twice.