The defender has not made a Premier League appearance since March 7 last year and has not featured in a matchday squad in any competition in 2020-21.
The 32-year-old is now free to speak to other clubs, with Sevilla, Real Betis and Genoa among those said to be interested.
In a statement posted on Twitter, Sokratis said: “One of the most enjoyable times in my career ended today.
“It has been an honour to wear the Arsenal shirt and I want to thank all the coaches, team-mates, staff and fans around the world for the love and respect they have given me.
“I gave everything for Arsenal and Arsenal also gave me a lot. I wish you all the best health and success always. Thank you.”
— Sokratis Papastathopoulos (@SokratisPapa5) January 20, 2021
Arsenal technical director Edu said: “On behalf of Mikel [Arteta], 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, whose deal had been due to expire at the end of the season, joined Arsenal from Borussia Dortmund in July 2018.
He made 69 appearances in all competitions for the Gunners, reaching the Europa League final in 2019 and winning the FA Cup last year.
In his time at the club, Sokratis won 57 tackles, 158 aerial duels and 314 duels, as well as making 248 clearances. Only Shkodran Mustafi ranks higher among Gunners defenders in that time.
Thank you, Papa
— Arsenal (@Arsenal) January 20, 2021
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