Aubameyang, 24, has joined the Champions League finalists on a five-year contract.
"We are very happy to have signed the player we most wanted in Pierre-Emerick Aubameyang," Dortmund's sporting director Michael Zorc told the club's website.
"He is very versatile in attack, plays at a high tempo and poses a goal threat."
Aubameyang, who joined St Etienne in 2011, scored 19 goals in Ligue 1 last season.
Aubameyang's arrival will increase speculation over the future of Robert Lewandowski, even though Dortmund have ruled out selling their star player this summer.
The Pole has been denied his wish of a move to Bayern Munich this summer, but Dortmund coach Jurgen Klopp expects his attitude to still be spot on next term.
"Lewandowski last season invested everything up until the final day into order to have maximum success," he told a press conference.
"He will also do that next year, because he is a footballer through and through.
"Nothing has happened, except that a player has said he would like to transfer somewhere else. We respect that there are such wishes. That is totally normal."