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|Benfica's Portuguese forward Joao Felix gestures during the Portuguese league football match. (MIGUEL RIOPA/AFP)|
The fee is a record for a Portuguese club and for Atletico Madrid and makes the teenager one of the five most expensive players in history.
Atletico tweeted a video of the player in the Prado gallery in Madrid contemplating paintings by old masters, with the phrase, "enormous talent", before he turned and smiled at the camera with the caption: "Welcome Joao Felix, pure talent."
Felix has reportedly signed a seven-year contract.
He is a potential replacement for Antoine Griezmann who scored 133 goals in five seasons at the club. Atletico have already said the French striker is leaving. He is expected to join Barcelona when his release clause, which dropped to €120 million on Monday, is activated.
The Felix signing came on a busy day for Atletico.
Earlier on Wednesday, the club confirmed the signing of Mexican midfielder Hector Herrera from Porto while another midfielder, Rodrigo Hernandez, left Madrid for Manchester City for €70 million.
Atletico had already bolstered their midfield with the addition of the 24-year-old Marcos Llorente, bought for €45 million from Real Madrid.
Felix, a forward who can play on either flank or centrally, has enjoyed a breakthrough season at Benfica, scoring 20 goals in 43 games and helping the club win the Portugese league title.
He also made his debut for Portugal earlier this month, starting alongside Cristiano Ronaldo in their Nations League semi-final win over Switzerland.
He had been linked with a number of Europe's leading clubs including Manchester City, Manchester United and Juventus.
Atletico coach Diego Simeone said in June that the Portuguese prodigy was in his sights.
"He's a young player," Simeone told Fox Sports Argentina. "Historically, Atletico Madrid is a club that buys young players in order to develop and improve them ... Like Griezmann, who when he arrived was not what he is today."
Felix becomes the most expensive Portuguese player in history, breaking the record of 105 million euros Juventus paid last summer for Ronaldo.
Atletico's previous record signing was French midfielder Thomas Lemar who joined last year from Monaco for €72 million.
The world transfer record is the €222 million Paris Saint-Germain paid Barcelona for Neymar in 2017.