The Ghana midfielder comes to London after the Gunners were able to complete a £45 million (€50m/$58m) deal ahead of Monday’s transfer deadline.
Arsenal had been linked to Partey for some time, with negotiations with Atleti proving difficult for the London club.
On Monday, though, the Gunners got their man, paying the midfielder's release clause to finally complete a deal for the 27-year-old star.
A statement from the Spanish capital club reads: “La Liga has communicated to Atletico Madrid this Monday at 11:28 pm that representatives of Arsenal appeared at the headquarters of the organisation in order to exercise the termination clause of the footballer Thomas Partey.
“As such, the player has unilaterally terminated the employment contract that bound him to our club until June 30, 2023.”
Partey had the first part of his medical in Madrid earlier on Monday before travelling to London to finalise his move to Arsenal.
Atletico did not want to lose the midfielder and had given him assurances that he will be handed a new contract once the financial difficulties brought on by the coronavirus pandemic begin to sort themselves out in the coming months.
However, Partey had wanted to seal a move to Arsenal, and has now been granted that move as he heads to the Premier League.
The Ghana midfielder had been one of Arsenal's primary targets all summer, along with Lyon midfielder Houssem Aouar, who confirmed this past weekend he will be staying with the French club for another year.
Partey had been with Atletico Madrid since 2011, making his full debut with the club in 2015 following loan spells to Mallorca and Almeria.
He went on to make 188 total appearances for Atleti, scoring 16 goals in the process.
During his time with the club, Partey claimed a Europa League and a UEFA Super Cup trophy while also featuring in Atletico's run to the 2015-16 Champions League final.
Last season, Partey featured 46 times in all competitions while further establishing himself as one of the top midfielders in La Liga in the process.
Internationally, the 27-year-old star has earned 27 caps for Ghana, having featured at two African Cup of Nations tournaments.
Arsenal defeated Sheffield United 2-1 over the weekend as the Gunners sit fourth in the Premier League heading into the international break.
Their next match comes on October 17, when they visit Manchester City.