The 23-year-old Portuguese joins Chelsea from Atletico Madrid for the remainder of the season, for a reported 11 million pounds.
Arsenal and Manchester United both ruled themselves out of the chase due to the price, with many critics taking aim at Blues owner Todd Boehly for the exorbitant fee paid for a loan deal.
The move comes as Felix extended his Atleti contract for a further season, until 2027, with no buy-out clause in the loan either.
Felix has struggled for goals at Atleti this term, leading to him falling out of the starting line-up and wanting a move.
“Chelsea is one of the great teams in the world and I hope to help the team reach their objectives - I’m very, very happy to be here and very excited to play at Stamford Bridge,” Felix said.
“Being here at Chelsea feels amazing, I’m very happy and I’ll bring my happiness of the game onto the pitch.
“Playing with happiness is what I’m about so I like to get on the ball and I want to make all the fans enjoy my football while helping the team.”
Under-fire Chelsea manager Graham Potter was delighted with his signing and said he’d be available immediately.
The Blues are due to take on Fulham in the Premier League on Thursday.
“He is a quality player,” Potter said. “He can make a difference in the final third of the pitch. Young, but has obviously still had a lot of really good experience so he is just a quality player who gives everybody a lift.
“He’s been training regularly, had game time so physically he can go in. There’s a little unknown with the adaptation period.”