"He has been given permission to attend the medical examination. The contract details and the financial plan are still to be clarified but I have no doubt that we will reach an agreement," Saint-Etienne club president Roland Romeyer said.
Dortmund's director Michael Zorc has been in France since Monday and confirmed they are in talks with the 24-year-old, who scored 19 goals and created 14 assists as Saint-Etienne finished fifth in Ligue 1 last season.
Aubameyang will sign a five-year deal worth €13m ($16.8m USD, £11m) and would be Dortmund's second new signing after Greek defender Sokratis, who cost €9.5m from Werder Bremen.
Both Bayer Leverkusen and Premier League side Newcastle United were said to also be chasing Aubameyang, who last season helped Saint-Etienne win their first trophy for 31 years.
Dortmund are in training at Kirchberg, Austria, until Saturday and have a pre-season tournament on 20 and 21 July hosted by Borussia Mönchengladbach and including Hamburger SV and European champions Bayern München.