Sokratis joined the Gunners from Borussia Dortmund in the summer of 2018 for a fee of around £17million, but had slipped down the defensive pecking order.
The centre-back found his opportunities limited last season and he was then left out of Mikel Arteta’s Europa League and Premier League squads in 2020/21.
The 32-year-old had six months left to run on his contract, but has now left Arsenal immediately after agreeing to a mutual termination.
Arsenal’s 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 - who made 69 appearances for Arsenal in total and won last season’s FA Cup in addition to reaching the 2019 Europa League final in Baku - is attracting interest from a number of clubs, including Serie A side Genoa, Greek giants Olympiacos and LaLiga outfit Real Betis.
"One of the most enjoyable times in my career ended today,” Sokraris tweeted. 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.
“One of the most enjoyable times in my career ended today,” Sokraris tweeted. ”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 is the latest player Arsenal have sought to get off their books this window as Arteta looks to trim his bloated squad.
Mesut Ozil has also mutually terminated his contract and is close to joining Fenerbahce in Turkey, while Sead Kolasinac has been loaned to former club Schalke.
William Saliba was also sent out on loan to Nice in Ligue 1.