Felix, now 25, made a blockbuster move from Benfica to Atletico Madrid in 2019, but has since seen his fortunes decline.
"I'm here to spread joy. Let's win together," said Felix in a video posted on the club's X account. A separate post said he had signed until 2027.
Felix remains one of the most expensive transfers in history, following his move to Atletico for 127.7 million euros (£110.5m) in 2019.
He has since had stints at Barcelona, AC Milan and Chelsea, but has failed to score more than 10 goals a season since leaving Benfica.