That left Sokratis free to join another club and he has now headed back to his native Greece to join Olympiakos.
The 32-year-old had been attracting interest from clubs around Europe, including Genoa in Italy and Spanish side Real Betis, but he has elected to go back home.
Sokratis has signed a contract until the summer of 2023.
After leaving Arsenal, 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.”