The former Porto youth player made his international debut against Switzerland in the Nations League semi-final in June.
He scored a hat-trick against Eintracht Frankfurt in the Europa League in April, becoming the youngest Benfica player and the youngest Portuguese footballer to score three goals in Europe and the youngest player ever to do so in the Europa League.
Atletico striker Antoine Griezmann has confirmed he will leave the club this summer, with Barcelona expected to pay his buyout clause of 120m euros.
On Wednesday, Atletico also confirmed the signings of two players from Porto.
Mexico midfielder Hector Herrera, 29, has signed a three-year deal after moving on a free transfer, while Brazil centre-back Felipe, 30, has joined for 20m euros (£17.9m).
Rodri: Manchester City pay £62.8m release clause for Atletico Madrid's Spain midfielder
Rodri previously played for Atletico Madrid's youth set up before joining Villarreal
Manchester City are set to sign Spain midfielder Rodri from Atletico Madrid for a club record £62.8m after paying his release clause, says the La Liga side.
Atletico said that the player's lawyers and representatives from City paid the release clause to La Liga on Wednesday.
Rodri, 23, has therefore terminated his contract with Atletico, which was due to run until June 2023.
It will beat City's previous record of £60m in signing Riyad Mahrez in 2018.
Rodri joined Atletico in May 2018 after three years at Villarreal and made 34 league appearances as they finished second in La Liga.
He made his international debut in a friendly against Germany last year and has made six senior international appearances.
City had made Rodri one of their main targets this summer with manager Pep Guardiola keen to sign a defensively-minded player to bolster the Premier League champions' squad.
Angelino rejoins City
On Wednesday City announced that they have brought full-back Angelino back to the club from PSV Eindhoven.
The 22-year-old Spaniard left City for PSV Eindhoven in 2018 after failing to make a Premier League appearance in his six years with the club.
City inserted a £5.35m buy-back clause in the deal, a figure far below the Spaniard's market value given his form at PSV last season.
Manager Pep Guardiola has decided to activate the clause in order to bolster his options at left-back, which also include Oleksandr Zinchenko, who signed a long-term contract earlier this summer, and Benjamin Mendy, a £52m arrival from Monaco in 2017.
Angelino has signed a four-year deal which will keep him at the Etihad Stadium until 2023.
"I expected that I would get a chance at Liverpool sooner. Before I came, we talked about it. They said that if I had a good first season, I had a good chance of joining the first team," he told Voetbalzone.nl.
"Due to injury, that did not come true. I had to undergo surgery at the start of my second season and then it is difficult to return."
Adekanye is reported to have signed a four-year contract with the Serie A side and has seemingly been given assurances over his participation in Simone Inzaghi's first team.
He had previously suggested that Barcelona were interested in signing him, although it is ultimately Lazio that he has decided to sign for.
He said in March: "They [Lazio] are one of the clubs that is interested, but it is not yet 100 per cent decided.
"I also heard from Barcelona. In the Netherlands, Willem II came by. I can't name the entire list of clubs now, because then we will be busy tomorrow. But there is interest from, among others, the Netherlands, Italy and Spain.
"In the summer I am going to talk about it with my family and business manager Junior Minguella, I am not worried that I will have no club."
Liverpool, who signed the Nigeria-born Dutch youth international from Barca in 2015, had been keen to extend Adekanye's deal at Anfield, with them being prepared to allow him to leave in January 2019 in order to gain first-team experience.