Arsenal have mutually agreed to terminate the contract of Sokratis.
The Greece international has not played in any competition for the Gunners this season after falling out of favour under boss Mikel Arteta.
He joined Arsenal for £17.6million in July 2018 from Borussia Dortmund and won the FA Cup during his time at the Emirates, making a total of 69 appearances.
And the club have confirmed he has now left.
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.”
The former AEK Athens defender, 32, is out of contract in the summer and is keen to secure a move away from north London this month.
He featured for the club’s Under-21s and U23s towards the end of last year in a bid to retain his sharpness ahead of a potential move away.
The news comes amid Mesut Ozil’s imminent move to Fenerbahce.
Like Sokratis, Ozil hasn’t featured for the Gunners this term, despite earning £350,000-a-week.
Ozil’s compatriot and former Arsenal teammate Lukas Podolski has hit out at the Gunners for their treatment of the World Cup-winning midfielder.
“I generally think with a player who is now in his sixth or seventh year with the club, to kick him completely out of the squad, that’s absolutely not okay,” Podolski said.
“He’s shown his class on the pitch, he’s never been negative towards his colleagues or the club. Arsenal as a club have not looked positive in this situation over the last months.”