Partey has been a long-term target for the Gunners, who were looking to bolster their options in central midfield.
“We have been watching Thomas for a while, so we’re now delighted to add such a high quality player to our squad,” said Arsenal manager Mikel Arteta.
“He is a dynamic midfielder with great energy. He brings a lot of experience from a top club that has competed at the highest level in La Liga and the Champions League for several years.”
Uruguayan international Lucas Torreira has gone the other way from Arsenal to Atletico on a season-long loan deal.
Atletico said in a statement: “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.
“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.
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 Arteta.
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.
“Thomas has all the right attributes to be a top player for Arsenal,” said the club’s technical director Edu. “He is a leader on and off the pitch and he is exactly the kind of player and person we want at the club.
“We already feel like we know Thomas very well based on the work we have done analysing his performances closely in recent times.
“With his all-round game and positive aggressive style, he will be a brilliant addition to our squad. We’ve made a strong start to the season and we want to continue to build on this with Thomas now part of our club.”
Partey join up with his new team-mates next week after he returns from international duty with Ghana.