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Partey has been a long-term target for the Gunners, who were looking to bolster their options in central midfield.
"La Liga informed Atletico de Madrid at 11.28pm on Monday that Arsenal representatives have paid Thomas Partey's release clause at the sports association's headquarters," Atletico said in a statement.
"The player has therefore unilaterally terminated his contract with our club, which ran until June 30, 2023."
Arsenal have made an impressive start to the season, winning three of their opening four Premier League games, as they aim to return to the Champions League next season for the first time in five years.
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However, the Londoners have been short in midfield with Mesut Ozil and Matteo Guendouzi, who has joined Hertha Berlin on a season-long loan, frozen out by Mikel Arteta.
Uruguayan international Lucas Torreira has gone the other way from Arsenal to Atletico on a season-long loan deal.
Partey was part of the Atletico sides that reached the 2016 Champions League final and beat Arsenal on the way to winning the Europa League in 2018.
A tough-tackling midfielder with an eye for goal, the 27-year-old scored 16 times in 188 appearances for Atletico since breaking into the first team in 2015.
kca/td