The Greece international last week had his Arsenal contract cancelled by mutual consent with six months left.
Sky in Italy had reported that Serie A side Genoa and Spain's Real Betis were interested in signing Sokratis but he has chosen to return to Greece to join Olympiakos. The 32-year-old, who joined Arsenal from Bundesliga club Borussia Dortmund in 2018, played 69 games in all competitions for the London side and helped them win the FA Cup last season.
Olympiakos are top of the Greek Super league with 48 points from 18 games, 11 points clear of second-placed AEK Athens.
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