A host of top clubs have been chasing the 19-year-old, but Atleti agreed to pay slightly over the release clause in his contract to win the race for his signature.
Felix has also penned a bumper seven-year deal with Atleti, who have sold Spain midfielder Rodri to Premier League champions Manchester City for £62.8m to help fund the deal.
The transfer makes Felix the fourth most expensive transfer in history, as only Neymar, Kylian Mbappe, Philippe Coutinho and Ousmane Dembele have moved for more money.
The 19-year-old only trails Neymar (199.80m, Barcelona-PSG), Philippe Coutinho (£130.50m, Liverpool-Barcelona) and Kylian Mbappe (£121.50m, Monaco-PSG) in the list of the biggest ever deals.
Eden Hazard's move to Real Madrid is reportedly set to rise to £150m in time once all bonus payments kick in but the flat fee was just shy of £100m.
Felix made his senior debut in August and scored 15 goals last season while he also made his international debut for Portugal during the Nations League semi-final victory over Switzerland in June.