The Portugal international joins Chelsea for an undisclosed fee, signing a deal to 2031 in the process.
"I’m really happy to be back at Chelsea and I can’t wait to get started," Felix told chelseafc.com. "I can see some familiar faces from the last time I was here, which is always nice.
"I loved my time here before and I told my friends and family that I’d love to return to the Premier League one day. To do that with Chelsea is a great feeling and I’m excited to be back."
Felix is happy to be back after a six month loan with Chelsea 18 months ago.
"It’s a chance for me to find a home," Felix also said.
"After two loans, Chelsea and Barca, I needed to stay permanently in one place. There is no better place for me to be than Chelsea. I see a perfect place to shine.
"It was a little bit of a lot of things that made me want to come back: the project, the club, the league, the fans, the time I spent here that I loved. I felt really good when I was here, despite the results we had. I’m really happy to be back.
"I’ve kind of changed since I was last here. I’m 24 now. I’ll be 25 in November. I feel like I grew up as a player. That’s normal with age. I’m more prepared for the Premier League.
"I feel like my best years are ahead of me. I have no doubt about that. The best years are still to come. And this year is going to be a good year, because now I am permanently at home, and I can enjoy home."