The Ghanian joins on a long-term contract after the Gunners activated his release clause on deadline day.
Partey had been a priority target for Mikel Arteta's side this summer and the club spent most of the window trying to negotiate a lower fee for the midfielder, but they decided to pay the release clause in full on Monday afternoon.
The move then progressed quickly, with the 27-yer-old completing his medical in the Spanish capital and at Arsenal's London Colney training ground before agreeing personal terms.
Partey becomes Arsenal's fifth and final signing of the summer after the arrivals of Willian, Gabriel Magalhaes, Dani Ceballos and Alex Runarsson.
The midfielder will wear the number 18 shirt and will join up with his new team-mates next week after he returns from international duty with Ghana.