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."