Sokratis was previously been linked with a move to Manchester United, but has instead opted to join Arsenal.
The 30-year-old defender has agreed a long-term contract at the club, with Arsenal paying a reported €20million for the Greece international.
Sokratis previously played for clubs including Werder Bremen, AC Milan, Genoa and AEK Athens but has been at Dortmund since 2013.
He helped the club to win the DFB-Pokal in the 2016-2017 season, also claiming a brace of DFL-Supercup crowns during his time at Dortmund.
Sokratis Papastathopoulos has described joining his old friends Pierre-Emerick Aubameyang and Henrikh Mkhitaryan at Arsenal as a "beautiful" moment.
It's very beautiful that I have come but I also have two players I was together with for a lot of years," he said to his new club's official website.
"I know them both very well and I'm very happy.
"I spoke [to them] a lot of times. They said to me the best things about this club - that it is one big family, and of course they also called me not every day but a lot of times telling me to come here.
Sokratis is the third player to join Arsenal since the appointment of Unai Emery as the club's new coach, following former Juventus full-back Stephan Lichtsteiner and goalkeeper Bernd Leno to Emirates Stadium.