Felix has extended his contract with Atletico by one year until the summer of 2027 before making the move.
There is no option-to-buy clause inserted in the contract for Chelsea, meaning Felix will head back to Spain at the end of the short-term deal.
The Portugal international has made 14 appearances in La Liga this season, scoring four goals and recording three assists.
Atletico made Felix the fifth most expensive signing in history when poaching him as a 19-year-old from Benfica in the summer of 2019 for £112m.
Chelsea have paid Atletico £10m to take Felix on loan.
The Blues have recently lost Armando Broja, Raheem Sterling and Christian Pulisic to injuries and need a spark in attack to improve upon their current 10th place standing in the Premier League.
On the loan move to Chelsea, Felix told the club's official website: "Chelsea is one of the great teams in the world and I hope to help the team reach their objectives, so I am very, very happy to be here and very excited to play at Stamford Bridge."
Felix is Chelsea's fourth signing this winter after Benoit Badiashile, Andrey Santos and David Datro Fofana.
Felix could make his debut at Craven Cottage on Thursday when Chelsea travel to face Fulham in the Premier League.
