The 27-year-old has decided the time is right to quit Dortmund after four years with the Bundesliga club in which time he established himself as one of the top strikers in Europe.
But a dream move to Real Madrid has failed to materialise, and now he has opted to make the switch to Paris.
German paper Bild say the player has now finalised his personal terms and the transfer is expected to be completed any day now.
Dortmund have reluctantly agreed to let one of their key players leave and have already started looking for his replacement.
Sports director Michael Zorc said: “We know that Auba is serious about his future. He will be 28 and the question is whether he wants to do something new again.”
Aubameyang has agreed a deal that will see him land a £5million signing on fee and be paid £8.75m-a-year in wages.