The Greek international defender joined from Borussia Dortmund in July 2018 but had fallen out of favour under Mikel Arteta and was no longer part of the Gunners' boss plans.
He follows Mesut Ozil in being allowed to leave the club this month with more to follow as Arteta reshapes his squad.
Technical director Edu said: “On behalf of Mikel, our coaches, players and everyone at the club, I would like to thank Papa for his contribution to the club.
"He has been an important part of our group and has been a model professional throughout. The negotiations to end his contract have been collaborative and we wish Papa and his family well for the future.”
Sokratis made 69 appearances for the club.
He was part of the FA Cup-winning squad last season and played 12 matches during the run to the Europa League final in 2019.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies