The Premier League club met his £45million release clause on transfer deadline day.
Partey signed a long-term deal with the Gunners, after he completed his medical and paperwork just before the 11 pm deadline.
He will wear the No 18 shirt at the Emirates and join up with his new team-mates next week after international duty with Ghana.
Mikel Arteta said: “We have been watching Thomas for a while, so we’re now delighted to add such a high quality player to our squad.
“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.”
Partey becomes Arsenal’s seventh signing of the summer, after Willian, Gabriel Magalhaes, Cedric Soares, Pablo Mari and goalkeeper Alex Runarsson.
The club also extended the loan deal for Dani Ceballos from Real Madrid for a second year.
