The Grece International has only played 7 games for the Rossoneri in the 2010/11 campaign before joining Werder Bremen.
Sokratis has also played 59 games with Genoa managing two goals over two campaigns.
The 30-year-old had also been linked with a return to the San Siro in the current transfer window but AC Milan’s financial struggles have prevented the Rossoneri from making any official deal for the former Borussia Dortmund center-back who has now joined the Gunners
According to reports in the UK, Arsenal has signed the Greek defender for £ 16 million (roughly € 20 million).
Sokratis won two Bundesliga titles and one German Cup during his five-year spell at Borussia Dortmund and Arsenal have announced that he will wear the number 5.