Diego Simeone's side paid a premium on Felix's €120-million release clause so they could make the payment in instalments.
He's the second-most expensive teenager following Kylian Mbappe, who cost Paris Saint-Germain a reported €180 million in 2018.
Felix registered 20 goals and 11 assists in 43 competitive matches last season, his first and only experience in top-flight football. He became the youngest player to score a hat-trick in the Europa League in April when he eviscerated Eintracht Frankfurt in a quarterfinal tie.
"With Felix's arrival, we add to our squad a versatile player who can play in any attacking position," read Atletico's statement. "He's a skillful footballer who can dribble and who's very good on the ball."
Griezmann's anticipated move to Barcelona and Rodri's departure to Manchester City will reportedly net Atletico close to €200 million in transfer fees, giving them the resources to splurge on Felix.
Atletico have now made five signings this summer. Felipe and Hector Herrera were announced as new arrivals earlier on Wednesday, while deals for Marcos Llorente and Renan Lodi were finalized last week.