The 27-year-old striker will join the French giants this summer after signing a £8.75m-per-year wages and a £5m signing-on fee.
A Gabon international, Aubameyang has been linked with Europe’s biggest clubs, including Liverpool, Man United and Real Madrid, but the French Cup and French League Cup holders appear to have secured his signing.
According to the report, only a few details need to be finalised before the 27-year-old links up with Edinson Cavani and Co in France.
Arsenal forward Alexis Sanchez is said to have been PSG’s top target this summer, but the Chilean has interest from Manchester City and Bayern Munich.
Aubameyang told Dortmund he wanted to leave this summer before helping his side beat Eintracht Frankfurt 2-1 in Saturday’s German Cup final.
Aubameyang scored 40 goals in all competitions last season, including the winner in the German Cup final, and clinched the Bundesliga Golden Boot with 31 goals, taking his tally to 120 goals in 189 matches in four seasons in Germany.