It is believed that the Gunners agreed a £17m fee with Dortmund back in June, but the north London club were unable to make the deal official until July due to the way in which the German financial year is structured.
Subsequently, Arsenal have been forced to wait before announcing the arrival of Sokratis, despite the Greek defender having already passed his medical at the club on Friday with no problems.
And, according to German news outlet RuhrNachrichten, Arsenal will be able to finally announce their acquisition of the 30-year-old defender now Dortmund's sporting director Michael Zorc has returned to work.
Following the appointment of Unai Emery as Arsene Wenger's successor, Sokratis will become Arsenal's third official signing of the summer, with the Gunners having already secured deals for Stephan Lichtsteiner and Bernd Leno, with a deal for Sampdoria's Lucas Torreira also reportedly in the pipeline.
Sokratis’ father, Charalambos, revealed on Greek radio last month that his son had turned down a potential move to Manchester United in order to complete a switch to the Emirates, saying: "There was interest from United but for July, he had to wait until July for United.
"United have a very good relationship with Dortmund, the teams speak a lot, but Sokratis chose to go to Arsenal."