The 24-year-old Aubameyang clocked 3.7 seconds over 30 metres during sprint training with the Champions League finalists this week, while Bolt ran 3.78sec over the same distance when he set the world 100m record of 9.58secs in Berlin in 2009.
"Pierre is definitely the fastest player who has ever played for us," Dortmund's director of sport Michael Zorc told German tabloid newspaper Bild.
The Gabon international is not only fleet-footed, as he proved scoring 41 goals and setting up a further 28, in 120 games for former club St Etienne.
He cost Dortmund €13 million (US$17m) from the French Cup winners.
"We're going to have a lot of fun playing alongside him," said Dortmund's Germany midfielder Ilkay Gundogan.
But Jamaica's sprint star may not be too happy that Dortmund have signed Aubameyang: Bolt is a fan of European champions Bayern Munich and friends with
their Germany star Bastian Schweinsteiger.
The 26-year-old sprinter is often in Munich as a patient of Bayern Munich's team doctor Hans-Wilhelm Müller-Wohlfahrt.