The Greece international said that he joined the Gunners because of their stature, history and fanbase.
"I feel very good. It's my first day here, everything is special. It's a beautiful moment and I'm very happy that I will be here for the next years," he told Arsenal's official website.
"Arsenal is one of the three biggest teams in the Premier League and one very big club. It has a lot of fans and a very big history.
"Like I said before, I'm very happy that for the next years I will be here to help the team."
Signed from Borussia Dortmund for an undisclosed fee, Sokratis has inked a "long-term" contract at the Emirates Stadium.