Partey signed a deal at the Emirates after he completed his medical and paperwork just before Monday’s 11pm deadline.
The Ghana international has been a key player in Diego Simeone’s midfield since breaking into the first team from Atletico’s academy in 2015.
He becomes Arsenal’s seventh signing of the summer, with the club having already signed Willian on a free transfer from Chelsea and defender Gabriel from Lille for £27m.
The Gunners also agreed permanent deals for defenders Cedric Soares and Pablo Mari, who had been on loan at the club, and extended the loan deal for Dani Ceballos from Real Madrid for a second year.
Goalkeeper Alex Runarsson was the club’s sixth signing, joining from Ligue 1 club Dijon on a four-year deal.
In recent weeks, Arsenal also moved for Lyon midfielder Houssem Aouar but after their offer was rejected they turned their attention back to the Atletico midfielder.
Lucas Torreira has moved in the opposite direction to Atletico Madrid in a loan deal until the end of the season and Matteo Guendouzi has signed for a German club Hertha Berlin on a season-long loan.